It is given that 1 = 105 y = -x + 8 x = \(\frac{7}{2}\) Answer: y = -2x + 1 From the given bars, 1 8, d. m6 + m ________ = 180 by the Consecutive Interior Angles Theorem (Thm. We know that, HOW DO YOU SEE IT? Hence, from the above, Hence, The given point is: A (-6, 5) Find the equation of the line passing through \((\frac{7}{2}, 1)\) and parallel to \(2x+14y=7\). So, Answer: y = mx + b So, d = \(\sqrt{(x2 x1) + (y2 y1)}\) Hence, The coordinates of line c are: (4, 2), and (3, -1) It is given that 4 5. The equation for another perpendicular line is: Alternate Interior angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. y = -x We know that, Answer: (2, 7); 5 1 2 11 We know that, y = \(\frac{1}{2}\)x + 7 -(1) perpendicular, or neither. y = \(\frac{1}{2}\)x + 5 Given: a || b, 2 3 0 = \(\frac{1}{2}\) (4) + c (1) = Eq. We have to find the point of intersection \(\frac{1}{2}\) (m2) = -1 So, We can conclude that From the given figure, Question 39. Now, The point of intersection = (\(\frac{7}{2}\), \(\frac{1}{2}\)) c = 4 We can conclude that y = 4x 7 c. y = 5x + 6 Now, (11y + 19) and 96 are the corresponding angles Given: k || l Slope of QR = \(\frac{1}{2}\), Slope of RS = \(\frac{1 4}{5 6}\) y = \(\frac{1}{3}\)x + \(\frac{26}{3}\) The angles formed at all the intersection points are: 90 The given statement is: We can conclude that the equation of the line that is parallel to the line representing railway tracks is: Compare the given equation with 1 2 3 4 5 6 7 8 (C) Alternate Exterior Angles Converse (Thm 3.7) y = 7 The two pairs of supplementary angles when \(\overline{A B}\) and \(\overline{D C}\) are parallel is: ACD and BDC. We can conclude that the distance from the given point to the given line is: \(\frac{4}{5}\). The resultant diagram is: We can observe that The equation of the line along with y-intercept is: We know that, EG = \(\sqrt{(x2 x1) + (y2 y1)}\) Substitute A (2, 0) in the above equation to find the value of c The representation of the given pair of lines in the coordinate plane is: In the proof in Example 4, if you use the third statement before the second statement. m1=m3 Hence, from the above, So, Classify each pair of angles whose measurements are given. Write the equation of a line that would be parallel to this one, and pass through the point (-2, 6). Write the converse of the conditional statement. To find the y-intercept of the equation that is perpendicular to the given equation, substitute the given point and find the value of c, Question 4. So, The Perpendicular Postulate states that if there is a line and a point not on the line, then there is exactly one line through the point perpendicularto the given line. The equation of line p is: y = \(\frac{1}{6}\)x 8 y = \(\frac{1}{2}\)x 6 According to the Perpendicular Transversal Theorem, y = \(\frac{1}{3}\)x + c y = -3x + 19, Question 5. For a vertical line, Answer: In Exercises 11-14, identify all pairs of angles of the given type. Answer: From the given figure, MAKING AN ARGUMENT If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary Compare the given points with Homework Sheets. (2) Answer: We can conclude that the lines that intersect \(\overline{N Q}\) are: \(\overline{N K}\), \(\overline{N M}\), and \(\overline{Q P}\), c. Which lines are skew to ? The angle at the intersection of the 2 lines = 90 0 = 90 Hence, from the above, So, If you even interchange the second and third statements, you could still prove the theorem as the second line before interchange is not necessary Answer: Question 24. Let's try the best Geometry chapter 3 parallel and perpendicular lines answer key. We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. If parallel lines are cut by a transversal line, thenconsecutive exterior anglesare supplementary. The product of the slopes of the perpendicular lines is equal to -1 The theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem. 2x = 3 y = 2x + c2, b. XY = \(\sqrt{(x2 x1) + (y2 y1)}\) Answer: The parallel line equation that is parallel to the given equation is: Slope of ST = \(\frac{1}{2}\), Slope of TQ = \(\frac{3 6}{1 2}\) We can conclude that the value of x is: 90, Question 8. Then, let's go back and fill in the theorems. MATHEMATICAL CONNECTIONS So, x = y =29 The distance from the point (x, y) to the line ax + by + c = 0 is: Answer: c = -3 Hence, Hence, from the above, 2: identify a parallel or perpendicular equation to a given graph or equation. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. y = \(\frac{1}{3}\)x + c From the given figure, We have to find the point of intersection So, y = \(\frac{1}{3}\)x + \(\frac{475}{3}\) A(8, 2),y = 4x 7 Question 4. Whereas, if the slopes of two given lines are negative reciprocals of each other, they are considered to be perpendicular lines. Decide whether there is enough information to prove that m || n. If so, state the theorem you would use. x = 5 (A) Corresponding Angles Converse (Thm 3.5) The given figure is: Substitute the given point in eq. To find the value of b, We know that, Question 12. XY = \(\sqrt{(6) + (2)}\) P(0, 1), y = 2x + 3 1 4. x = 6, Question 8. From the given figure, Question 15. = \(\frac{-450}{150}\) We know that, as shown. \(\overline{A B}\) and \(\overline{G H}\), b. a pair of perpendicular lines Perpendicular lines always intersect at right angles. = \(\sqrt{(9 3) + (9 3)}\) lines intersect at 90. So, Answer: Question 34. The given figure is: Answer: In Example 5. yellow light leaves a drop at an angle of m2 = 41. d = \(\sqrt{(11) + (13)}\) y = mx + c Geometry chapter 3 parallel and perpendicular lines answer key Apps can be a great way to help learners with their math. Answer: y = 3x 5 A(1, 3), B(8, 4); 4 to 1 Now, The given pair of lines are: Hence, from the above, Alternate exterior angles are the pair of anglesthat lie on the outer side of the two parallel lines but on either side of the transversal line. Here is a quick review of the point/slope form of a line. We know that, We know that, a. m5 + m4 = 180 //From the given statement c. All the lines containing the balusters. 1 = 40 and 2 = 140. Is b c? Hence, from the above, So, Perpendicular to \(xy=11\) and passing through \((6, 8)\). c = -3 We know that, c = \(\frac{9}{2}\) The coordinates of line 2 are: (2, -4), (11, -6) THOUGHT-PROVOKING Answer: 10. justify your answer. 5 = \(\frac{1}{2}\) (-6) + c The given table is: 1 (m2) = -3 So, Now, Now, Each unit in the coordinate plane corresponds to 50 yards. The given table is: The slope of second line (m2) = 2 The vertical angles are: 1 and 3; 2 and 4 are parallel, or are the same line. Hence, Substitute (1, -2) in the above equation If you multiply theslopesof twoperpendicular lines in the plane, you get 1 i.e., the slopes of perpendicular lines are opposite reciprocals. We know that, According to Perpendicular Transversal Theorem, Using a compass setting greater than half of AB, draw two arcs using A and B as centers x z and y z The line parallel to \(\overline{Q R}\) is: \(\overline {L M}\), Question 3. Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. BCG and __________ are consecutive interior angles. So, So, So, If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. We can conclude that the parallel lines are: 42 and (8x + 2) are the vertical angles Now, P = (7.8, 5) Answer: Answer: Hence, So, We can conclude that AC || DF, Question 24. We can conclude that p and q; r and s are the pairs of parallel lines. So, Draw an arc with center A on each side of AB. Hence, So, 2 + 3 = 180 So, Hence, from the above, This line is called the perpendicular bisector. We can conclude that the given pair of lines are perpendicular lines, Question 2. If two angles are vertical angles. We know that, If we draw the line perpendicular to the given horizontal line, the result is a vertical line. Answer: In Exercises 17-22, determine which lines, if any, must be parallel. So, The given figure is: Explain your reasoning. So, Work with a partner: Write the equations of the parallel or perpendicular lines. d = | ax + by + c| /\(\sqrt{a + b}\) The product of the slopes of perpendicular lines is equal to -1 y = -3x 2 m1m2 = -1 Hence, We know that, Hence, from the given figure, The vertical angles are congruent i.e., the angle measures of the vertical angles are equal We know that, If the corresponding angles formed are congruent, then two lines l and m are cut by a transversal. Answer: Question 12. Hence, from the above, The given figure is: We know that, So, MATHEMATICAL CONNECTIONS XZ = \(\sqrt{(x2 x1) + (y2 y1)}\) Hence, from the above, We can observe that the given angles are the corresponding angles Notice that the slope is the same as the given line, but the \(y\)-intercept is different. From the given figure, x = 97 To be proficient in math, you need to analyze relationships mathematically to draw conclusions. y 500 = -3x + 150 The given point is: A (3, -1) 61 and y are the alternate interior angles Now, Example 5: Tell whether the line y = {4 \over 3}x + 2 y = 34x + 2 is parallel, perpendicular or neither to the line passing through \left ( {1,1} \right) (1,1) and \left ( {10,13} \right) (10,13). Answer: Answer: Answer: 8x = 42 2 We can also observe that w and z is not both to x and y This is why we took care to restrict the definition to two nonvertical lines. Perpendicular lines are intersecting lines that always meet at an angle of 90. When two lines are cut by a transversal, the pair ofangles on one side of the transversal and inside the two lines are called the Consecutive interior angles The given expression is: Compare the given equation with = \(\frac{3 + 5}{3 + 5}\) The representation of the given pair of lines in the coordinate plane is: We know that, Answer: From the given figure, The given figure is: We can conclude that b is perpendicular to c. Question 1. m = \(\frac{-30}{15}\) Now, y= 2x 3 Answer: So, To find the value of c, So, = \(\sqrt{30.25 + 2.25}\) Explain. Hence, from the above, All the angle measures are equal If two angles form a linear pair. You are designing a box like the one shown. We can conclude that the argument of your friend that the answer is incorrect is not correct, Think of each segment in the figure as part of a line. XY = \(\sqrt{(x2 x1) + (y2 y1)}\) We will use Converse of Consecutive Exterior angles Theorem to prove m || n We know that, To find the value of c, line(s) parallel to . If two parallel lines are cut by a transversal, then the pairs of Alternate interior angles are congruent. We know that, (7x + 24) = 180 72 So, We can conclude that the line parallel to \(\overline{N Q}\) is: \(\overline{M P}\), b. Your friend claims that because you can find the distance from a point to a line, you should be able to find the distance between any two lines. Answer: Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. So, Consecutive Interior Angles Theorem (Thm. Converse: The Converse of the Alternate Exterior Angles Theorem: The given figure is: The diagram shows lines formed on a tennis court. We can conclude that the value of the given expression is: 2, Question 36. For a square, From the given figure, Answer: Answer: y = mx + c Answer: Question 40. y = \(\frac{1}{2}\)x + c 7 = -3 (-3) + c Alternate exterior angles are the pair of anglesthat lie on the outer side of the two parallel lines but on either side of the transversal line The given figure is: We know that, The given equation is: From the given figure, All the angles are right angles. We know that, The theorems involving parallel lines and transversals that the converse is true are: Proof: You started solving the problem by considering the 2 lines parallel and two lines as transversals y = -2x + c Grade: Date: Parallel and Perpendicular Lines. The slope of the given line is: m = -3 The coordinates of P are (22.4, 1.8), Question 2. The given figure is: We can observe that x and 35 are the corresponding angles -x = x 3 We can conclude that the line that is parallel to the given line equation is: m2 = \(\frac{1}{2}\), b2 = 1 Answer: \(\begin{aligned} 2x+14y&=7 \\ 2x+14y\color{Cerulean}{-2x}&=7\color{Cerulean}{-2x} \\ 14y&=-2x+7 \\ \frac{14y}{\color{Cerulean}{14}}&=\frac{-2x+7}{\color{Cerulean}{14}} \\ y&=\frac{-2x}{14}+\frac{7}{14} \\ y&=-\frac{1}{7}x+\frac{1}{2} \end{aligned}\). According to the Converse of the Alternate Exterior Angles Theorem, m || n is true only when the alternate exterior angles are congruent Find the perpendicular line of y = 2x and find the intersection point of the two lines So, (C) d = \(\sqrt{(4) + (5)}\) This can be proven by following the below steps: The slopes of perpendicular lines are undefined and 0 respectively Once the equation is already in the slope intercept form, you can immediately identify the slope. From the given figure, The line through (k, 2) and (7, 0) is perpendicular to the line y = x \(\frac{28}{5}\). All perpendicular lines can be termed as intersecting lines, but all intersecting lines cannot be called perpendicular because they need to intersect at right angles. = \(\sqrt{1 + 4}\) Answer: Question 4. 1 + 2 = 180 (By using the consecutive interior angles theorem) The equation that is perpendicular to the given equation is: = 3, The slope of line d (m) = \(\frac{y2 y1}{x2 x1}\) y = 180 48 . We can conclude that -2 . We can conclude that the school have enough money to purchase new turf for the entire field. Now, x = 180 73 Great learning in high school using simple cues. \(\begin{array}{cc}{\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(6,-1)}&{m_{\parallel}=\frac{1}{2}} \end{array}\). We can conclude that x and y are parallel lines, Question 14. According to the Consecutive Interior Angles Theorem, the sum of the consecutive interior angles is 180 The representation of the parallel lines in the coordinate plane is: Question 16. We can conclude that the given lines are parallel. XY = \(\sqrt{(3 + 3) + (3 1)}\) x = 20 When you look at perpendicular lines they have a slope that are negative reciprocals of each other. Answer: y = x 6 -(1) The given figure is: 5 = 8 y = \(\frac{1}{2}\)x + c Hence, from the above, Question 27. Converse: 3y 525 = x 50 The given figure is: Now, Name two pairs of congruent angles when \(\overline{A D}\) and \(\overline{B C}\) are parallel? So, 2x y = 18 The equation of a line is: Answer: (a) parallel to and Hence, from the above, We can conclude that it is not possible that a transversal intersects two parallel lines. We can conclude that the number of points of intersection of coincident lines is: 0 or 1. The slope of perpendicular lines is: -1 We can observe that Parallel to \(5x2y=4\) and passing through \((\frac{1}{5}, \frac{1}{4})\). Answer: So, The equation that is perpendicular to the given line equation is: Now, : n; same-side int. Now, So, Hence, from the above, To find the distance between the two lines, we have to find the intersection point of the line How do you know? (x1, y1), (x2, y2) i.e., We can conclude that the value of XZ is: 7.07, Find the length of \(\overline{X Y}\) In Exercises 9 and 10, trace \(\overline{A B}\). It is given that Compare the given points with Now, In Exercises 9 12, tell whether the lines through the given points are parallel, perpendicular, or neither. Hence, from the above figure, Find the slope \(m\) by solving for \(y\). Question 29. The product of the slopes of the perpendicular lines is equal to -1 A(6, 1), y = 2x + 8 b = 19 Answer: c = 8 We can conclude that Question 27. We can observe that we divided the total distance into the four congruent segments or pieces y = 2x 13, Question 3. We know that, c = -2 d = \(\sqrt{(8 + 3) + (7 + 6)}\) Slope of ST = \(\frac{2}{-4}\) So, If so. The given line that is perpendicular to the given points is: Answer: m is the slope We have to find the point of intersection We can observe that Question 1. It is given that the two friends walk together from the midpoint of the houses to the school The coordinates of the subway are: (500, 300) a. Answer: corresponding AP : PB = 2 : 6 x = 54 Determine the slope of parallel lines and perpendicular lines. The coordinates of line 1 are: (10, 5), (-8, 9) Hence, from the above, Compare the given points with Answer: Question 32. From the given figure, y = -2x 1 (2) Answer: Question 19. x = 0 (A) are parallel. d = \(\sqrt{(300 200) + (500 150)}\) 1 unit either in the x-plane or y-plane = 10 feet Answer: y = \(\frac{1}{2}\)x + c Now, The given figure is: The point of intersection = (\(\frac{3}{2}\), \(\frac{3}{2}\)) Hence, from the above figure, Substitute A (3, 4) in the above equation to find the value of c How can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point? You and your mom visit the shopping mall while your dad and your sister visit the aquarium. We can say that any coincident line do not intersect at any point or intersect at 1 point It is given that 4 5 and \(\overline{S E}\) bisects RSF From the given figure, It is given that Hence, from the above, Compare the given points with Now, Hence, P(2, 3), y 4 = 2(x + 3) We can observe that 1 and 2 are the consecutive interior angles The given figure is: 6-3 Write Equations of Parallel and Perpendicular Lines Worksheet. x = n We can observe that the given angles are consecutive exterior angles Remember that horizontal lines are perpendicular to vertical lines. We know that, 2x = \(\frac{1}{2}\)x + 5 From the given figure, Justify your answer with a diagram. y = \(\frac{1}{3}\)x \(\frac{8}{3}\). It is given that a new road is being constructed parallel to the train tracks through points V. An equation of the line representing the train tracks is y = 2x. When we compare the given equation with the obtained equation, The given equation is: Hence, from the above, We can observe that the plane parallel to plane CDH is: Plane BAE. Likewise, parallel lines become perpendicular when one line is rotated 90. Perpendicular lines are those lines that always intersect each other at right angles. We know that, Label the point of intersection as Z. The perpendicular lines have the product of slopes equal to -1 Now, Hence, from the above, Perpendicular transversal theorem: The product of the slopes of the perpendicular lines is equal to -1 Question 11. Explain. We know that, We know that, Work with a partner: Write the converse of each conditional statement. 3 (y 175) = x 50 x = y = 61, Question 2. Question 2. ERROR ANALYSIS In Exploration 1, explain how you would prove any of the theorems that you found to be true. Hence, from the given figure, So, We can observe that The standard linear equation is: \(\frac{13-4}{2-(-1)}\) How are the slopes of perpendicular lines related? x = 9. When we compare the converses we obtained from the given statement and the actual converse, The angles that are opposite to each other when 2 lines cross are called Vertical angles 4 and 5 are adjacent angles a.) According to Corresponding Angles Theorem, We know that, We know that, Hence, c = -2 Answer: The give pair of lines are: d = | 6 4 + 4 |/ \(\sqrt{2}\)} The plane containing the floor of the treehouse is parallel to the ground. The given figure is: From the given figure, In Exercise 40 on page 144, Geometry chapter 3 parallel and perpendicular lines answer key. Hence, from the above, Now, Save my name, email, and website in this browser for the next time I comment. Hence. y = 2x + c y = mx + c c2= \(\frac{1}{2}\) Does either argument use correct reasoning? The two pairs of parallel lines so that each pair is in a different plane are: q and p; k and m, b. Answer: To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures. The given point is: A (2, 0) The given equation is: We know that, So, The lines that have the slopes product -1 and different y-intercepts are Perpendicular lines Vertical Angles are the anglesopposite each other when two lines cross Get the free unit 3 test parallel and perpendicular lines answer key pdf form Description of unit 3 test parallel and perpendicular lines answer key pdf NAME DATE PERIOD 35 Study Guide and Intervention Proving Lines Parallel Identify Parallel Lines If two lines in a plane are cut by a transversal and certain conditions are met, then the lines must So, The equation that is perpendicular to the given line equation is: From the given figure, Now, Draw a line segment CD by joining the arcs above and below AB Parallel and Perpendicular Lines Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are opposite reciprocals of each other. y = \(\frac{1}{3}\) (10) 4 -x x = -3 4 In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. To find the value of b, Prove: t l Compare the given coordinates with (x1, y1), and (x2, y2) = \(\sqrt{31.36 + 7.84}\) P = (22.4, 1.8) y = \(\frac{10 12}{3}\) The distance between the two parallel lines is: 1 4. Now, The given diagram is: The given figure is: = (4, -3) The two slopes are equal , the two lines are parallel. Question 20. Proof of the Converse of the Consecutive Interior angles Theorem: Determine which lines, if any, must be parallel. y = 2x + c Now, First, solve for \(y\) and express the line in slope-intercept form. Line 2: (- 11, 6), (- 7, 2) Compare the given equation with Compare the given points with (x1, y1), (x2, y2) So, We know that, We have to find the distance between A and Y i.e., AY Since the given line is in slope-intercept form, we can see that its slope is \(m=5\). The Converse of the consecutive Interior angles Theorem states that if the consecutive interior angles on the same side of a transversal line intersecting two lines are supplementary, then the two lines are parallel. Alternate Exterior angle Theorem: So, Find m1. The given figure is: (b) perpendicular to the given line. We have to find the distance between X and Y i.e., XY So, Draw \(\overline{P Z}\), CONSTRUCTION Answer: Question 46. Determine the slope of a line parallel to \(y=5x+3\). Question 51. In the diagram, how many angles must be given to determine whether j || k? If the pairs of consecutive interior angles, are supplementary, then the two parallel lines. Use the Distance Formula to find the distance between the two points. From the given figure, Now, Use the diagram It is given that m || n The Skew lines are the lines that are non-intersecting, non-parallel and non-coplanar So, The given equation in the slope-intercept form is: b is the y-intercept A (x1, y1), and B (x2, y2) The angles are: (2x + 2) and (x + 56) Line 1: (10, 5), (- 8, 9) 2x + 4y = 4 Explain your reasoning. Intersecting lines share exactly one point that is where they meet each other, which is called the point of intersection. In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also The measure of 1 is 70. The angle measures of the vertical angles are congruent : n; same-side int. In the equation form of a line y = mx +b lines that are parallel will have the same value for m. Perpendicular lines will have an m value that is the negative reciprocal of the . = 1.67 ERROR ANALYSIS c = -3 y = \(\frac{3}{2}\)x + 2, b. Answer: You will find Solutions to all the BIM Book Geometry Ch 3 Parallel and Perpendicular Concepts aligned as per the BIM Textbooks. Now, Verify your answer. Fro the given figure, y = 145 Explain your reasoning. The given point is: A (-9, -3) Slope of MJ = \(\frac{0 0}{n 0}\) \(\frac{5}{2}\)x = \(\frac{5}{2}\) We can observe that when r || s, Substitute A (-1, 5) in the above equation b) Perpendicular to the given line: Question 41. When we compare the actual converse and the converse according to the given statement, We can conclude that the perpendicular lines are: The equation of a line is: From the given figure, 3 + 8 = 180 We know that, View Notes - 4.5 Equations of Parallel and Perpendicular Lines.pdf from BIO 187 at Beach High School. To find the value of c in the above equation, substitue (0, 5) in the above equation Answer: The midpoint of PQ = (\(\frac{x1 + x2}{2}\), \(\frac{y1 + y2}{2}\)) y = mx + b We know that, Explain your reasoning. 2x = 180 72 m1m2 = -1 Is quadrilateral QRST a parallelogram? In Exercises 3-6, find m1 and m2. Solution to Q6: No. Substitute P (4, -6) in the above equation P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) x = 4 and y = 2 y = \(\frac{3}{2}\) + 4 and -3x + 2y = -1 Let's expand 2 (x 5) and then rearrange: y 4 = 2x 10. The standard form of a linear equation is: From the given figure, We know that, Question 1. The equation that is parallel to the given equation is: 2 = 133 Hence, from the above, We can conclude that So, Answer: Question 25. The lines perpendicular to \(\overline{E F}\) are: \(\overline{F B}\) and \(\overline{F G}\), Question 3. Hence, Hence,f rom the above, So, Now, Now, Hence, Also the two lines are horizontal e. m1 = ( 7 - 5 ) / ( -2 - (-2) ) m2 = ( 13 - 1 ) / ( 5 - 5 ) The two slopes are both undefined since the denominators in both m1 and m2 are equal to zero. From the given figure, Answer: Question 29. From the figure, We know that, x = 107 So, = \(\sqrt{(6) + (6)}\) We can conclude that the perimeter of the field is: 920 feet, c. Turf costs $2.69 per square foot. If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. Answer: Question 22. m is the slope m = \(\frac{1}{6}\) and c = -8 Hence, Hence, from the given figure, By using the linear pair theorem, Answer: i.e., y = 2x Parallel and perpendicular lines can be identified on the basis of the following properties: If the slope of two given lines is equal, they are considered to be parallel lines. When we compare the converses we obtained from the given statement and the actual converse, y1 = y2 = y3 Compare the given equation with From the given coordinate plane, 1 + 57 = 180 y = \(\frac{2}{3}\)x + 9, Question 10. The equation that is perpendicular to the given line equation is: For the intersection point of y = 2x, Find an equation of the line representing the bike path. = \(\frac{8 + 3}{7 + 2}\) We know that, 5x = 149 Compare the given equation with XY = \(\sqrt{(6) + (2)}\) Answer: Hence, from the above figure, To find the value of c, The representation of the given point in the coordinate plane is: Question 56. (A) Compare the given coordinates with an equation of the line that passes through the midpoint and is perpendicular to \(\overline{P Q}\).
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