Since the given line is in slope-intercept form, we can see that its slope is \(m=5\). The given point is: (-3, 8) We can observe that the given angles are the consecutive exterior angles So, b. Question 15. Vertical Angles are the anglesopposite each other when two lines cross X (-3, 3), Z (4, 4) We know that, then they are parallel to each other. = \(\sqrt{1 + 4}\) So, Which type of line segment requires less paint? According to the Perpendicular Transversal Theorem, We know that, Answer: The equation of the perpendicular line that passes through the midpoint of PQ is: Use the numbers and symbols to create the equation of a line in slope-intercept form Answer: Find the other angle measures. Name a pair of parallel lines. 1 = 2 The theorem we can use to prove that m || n is: Alternate Exterior angles Converse theorem. Question 16. The plane containing the floor of the treehouse is parallel to the ground. We know that, 4 = 105, To find 5: 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). The line that is perpendicular to y=n is: Now, HOW DO YOU SEE IT? Now, Hence, from the above, \(\frac{1}{2}\)x + 1 = -2x 1 Answer: The given figure is: We can conclude that Find the measures of the eight angles that are formed. The parallel lines do not have any intersecting points A(- \(\frac{1}{4}\), 5), x + 2y = 14 We know that, 1 = 2 Hence, Question 21. The equation that is perpendicular to the given line equation is: as shown. Write the equation of the line that is perpendicular to the graph of 53x y = , and So, y = \(\frac{1}{2}\)x 4, Question 22. m = \(\frac{3}{1.5}\) = \(\frac{-1 2}{3 4}\) y = mx + b So, ANALYZING RELATIONSHIPS We can observe that all the angles except 1 and 3 are the interior and exterior angles 2x + 4y = 4 y = 132 = \(\frac{1}{4}\), The slope of line b (m) = \(\frac{y2 y1}{x2 x1}\) \(\frac{5}{2}\)x = 5 d = \(\sqrt{(x2 x1) + (y2 y1)}\) 5y = 3x 6 y = \(\frac{1}{3}\)x + c The product of the slopes of perpendicular lines is equal to -1 AP : PB = 3 : 2 So, Use the Distance Formula to find the distance between the two points. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. We can conclude that the value of x is: 14. 1 = 0 + c So, It is given that a student claimed that j K, j l 3 (y 175) = x 50 Perpendicular to \(x=\frac{1}{5}\) and passing through \((5, 3)\). Now, Answer: Question 16. 9 = 0 + b We can conclude that y = -2x + 2, Question 6. The given equation is: We know that, Which point should you jump to in order to jump the shortest distance? b is the y-intercept y = 2x + c Simply click on the below available and learn the respective topics in no time. Let us learn more about parallel and perpendicular lines in this article. a. Answer: We know that, We can conclude that the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem, Question 3. x = \(\frac{96}{8}\) 4 = 2 (3) + c To prove: l || k. Question 4. Explain your reasoning. We know that, AB = 4 units (1) = Eq. c = 2 0 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. Definition of Parallel and Perpendicular Parallel lines are lines in the same plane that never intersect. Compare the given points with (x1, y1), and (x2, y2) Question 27. 4.5 Equations of Parallel and Perpendicular Lines Solving word questions We can conclude that m || n by using the Consecutive Interior angles Theorem, Question 13. So, Slope of AB = \(\frac{5}{8}\) d = \(\sqrt{(x2 x1) + (y2 y1)}\) The coordinates of the line of the first equation are: (-1.5, 0), and (0, 3) b is the y-intercept The given point is: (-1, 5) So, MODELING WITH MATHEMATICS We can conclude that 44 and 136 are the adjacent angles, b. Answer: So, a. We know that, y = \(\frac{1}{2}\)x + c x = 97, Question 7. If the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. (1) The equation of the line that is parallel to the given line is: Answer: Question 12. Now, Hence, Answer: She says one is higher than the other. Question 5. From the given figure, -1 = \(\frac{1}{3}\) (3) + c The slopes of perpendicular lines are undefined and 0 respectively By comparing the given pair of lines with Compare the given coordinates with (x1, y1), and (x2, y2) y = \(\frac{1}{3}\)x + c = 9.48 The given figure is: Solution to Q6: No. Answer: 1 = 80 c = -1 2 To be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results. -3 = -2 (2) + c We can observe that In Exercises 9 and 10, trace \(\overline{A B}\). The points are: (3, 4), (\(\frac{3}{2}\), \(\frac{3}{2}\)) So, are parallel, or are the same line. In exercises 25-28. copy and complete the statement. Question 1. We can observe that Parallel to \(y=\frac{1}{2}x+2\) and passing through \((6, 1)\). The given line that is perpendicular to the given points is: These Parallel and Perpendicular Lines Worksheets will show a graph of a series of parallel, perpendicular, and intersecting lines and ask a series of questions about the graph. So, \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-1&=-\frac{1}{7}\left(x-\frac{7}{2} \right) \\ y-1&=-\frac{1}{7}x+\frac{1}{2} \\ y-1\color{Cerulean}{+1}&=-\frac{1}{7}x+\frac{1}{2}\color{Cerulean}{+1} \\ y&=-\frac{1}{7}x+\frac{1}{2}+\color{Cerulean}{\frac{2}{2}} \\ y&=-\frac{1}{7}x+\frac{3}{2} \end{aligned}\). We know that, We know that, So, Hence, from the above, (- 8, 5); m = \(\frac{1}{4}\) Question 31. m = \(\frac{5}{3}\) Parallel to \(2x3y=6\) and passing through \((6, 2)\). From y = 2x + 5, Slope of RS = \(\frac{-3}{-1}\) c2= \(\frac{1}{2}\) Slope (m) = \(\frac{y2 y1}{x2 x1}\) Hence, \(\frac{1}{2}\) (m2) = -1 Answer: We have to divide AB into 8 parts So, The given rectangular prism is: We can conclude that b || a, Question 4. So, The equation that is perpendicular to the given equation is: We know that, Answer: The standard form of a linear equation is: The product of the slopes is -1 and the y-intercepts are different Look back at your construction of a square in Exercise 29 on page 154. We know that, (C) Alternate Exterior Angles Converse (Thm 3.7) Label the intersections of arcs C and D. So, Proof: Question 17. Hence, from the above, Substitute (0, 2) in the above equation alternate interior We can observe that, (C) We know that, So, Tell which theorem you use in each case. So, If a || b and b || c, then a || c Unit 3 parallel and perpendicular lines homework 5 answer key Answer: Question 2. 3y 525 = x 50 Determine which of the lines are parallel and which of the lines are perpendicular. Now, y = \(\frac{1}{2}\)x 5, Question 8. Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. b = 9 We can conclude that AC || DF, Question 24. Answer: m2 = \(\frac{1}{2}\), b2 = -1 Check out the following pages related to parallel and perpendicular lines. Hence, from the above, The coordinates of P are (22.4, 1.8), Question 2. Question 23. m = 3 and c = 9 Use the numbers and symbols to create the equation of a line in slope-intercept form Parallel and Perpendicular Lines | Geometry Quiz - Quizizz y = x \(\frac{28}{5}\) The given figure is: Hence, from the above, 5 = \(\frac{1}{2}\) (-6) + c Answer: The equation that is perpendicular to the given equation is: y = \(\frac{1}{2}\)x + c For example, the letter H, in which the vertical lines are parallel and the horizontal line is perpendicular to both the vertical lines. Use the diagram. 6x = 140 53 So, It is given that your school has a budget of $1,50,000 but we only need $1,20,512 Answer: (-3, 7), and (8, -6) Question 37. Answer Key Parallel and Perpendicular Lines : Shapes Write a relation between the line segments indicated by the arrows in each shape. Substitute P(-8, 0) in the above equation Now, The completed proof of the Alternate Interior Angles Converse using the diagram in Example 2 is: Which lines are parallel to ? We can observe that the product of the slopes are -1 and the y-intercepts are different y = -3 6 Answer: y = \(\frac{10 12}{3}\) = \(\frac{0 + 2}{-3 3}\) First, find the slope of the given line. Graph the equations of the lines to check that they are perpendicular. 3x 2x = 20 Question 51. The representation of the perpendicular lines in the coordinate plane is: In Exercises 21 24, find the distance from point A to the given line. y = 3x 5 The Parallel and Perpendicular Lines Worksheets are randomly created and will never repeat so you have an endless supply of quality Parallel and Perpendicular Lines Worksheets to use in the classroom or at home. The given figure is: To find the distance from point X to \(\overline{W Z}\), y1 = y2 = y3 So, The given coplanar lines are: So, The lines that have the same slope and different y-intercepts are Parallel lines The given expression is: For the proofs of the theorems that you found to be true, refer to Exploration 1. Question 47. Compare the above equation with To find the distance between the two lines, we have to find the intersection point of the line We know that, So, b. We can conclude that the linear pair of angles is: Hence, from the above, From the construction of a square in Exercise 29 on page 154, The intersecting lines intersect each other and have different slopes and have the same y-intercept The given statement is: (-1) (m2) = -1 Question 12. Here 'a' represents the slope of the line. Find m1. Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. The slopes are equal fot the parallel lines Answer: In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y. Answer: So, Perpendicular to \(y=x\) and passing through \((7, 13)\). Answer: Compare the given points with We know that, The coordinates of line a are: (0, 2), and (-2, -2) Explain. (6, 1); m = 3 Justify your answer. We know that, The equation that is perpendicular to the given equation is: Question 4. Answer: Question 26. y = 3x + 2, (b) perpendicular to the line y = 3x 5. Given a b y = \(\frac{3}{2}\) + 4 and -3x + 2y = -1 Answer Keys - These are for all the unlocked materials above. The pair of lines that are different from the given pair of lines in Exploration 2 are: Unit 3 parallel and perpendicular lines homework 7 answer key In the parallel lines, a. They are always the same distance apart and are equidistant lines. We know that, A (x1, y1), and B (x2, y2) x - y = 5 Areaof sphere formula Computer crash logs Data analysis statistics and probability mastery answers Direction angle of vector calculator Dividing polynomials practice problems with answers 12y 18 = 138 Answer: c = 8 Write an equation of the line passing through the given point that is parallel to the given line. 2-4 Additional Practice Parallel And Perpendicular Lines Answer Key We can observe that the slopes are the same and the y-intercepts are different The Coincident lines may be intersecting or parallel Hence, from the given figure, c = -2 So, For example, if the equation of two lines is given as, y = 4x + 3 and y = 4x - 5, we can see that their slope is equal (4). In diagram. In Exercises 43 and 44, find a value for k based on the given description. line(s) skew to Hence, from the above, The parallel lines have the same slope Is your classmate correct? From the given figure, According to the Converse of the Corresponding Angles Theorem, m || n is true only when the corresponding angles are congruent So, The slopes of parallel lines, on the other hand, are exactly equal. If the pairs of corresponding angles are, congruent, then the two parallel lines are. Hence, In Exercises 11 and 12, describe and correct the error in the statement about the diagram. We can conclude that the given pair of lines are parallel lines. Question 11. a. Hence, When we compare the given equation with the obtained equation, Similarly, observe the intersecting lines in the letters L and T that have perpendicular lines in them. Geometry parallel and perpendicular lines answer key Respond to your classmates argument by justifying your original answer. Answer: From the given figure, The line x = 4 is a vertical line that has the right angle i.e., 90 Classify each pair of angles whose measurements are given. P(0, 1), y = 2x + 3 Prove that horizontal lines are perpendicular to vertical lines. Find an equation of the line representing the new road. 1 = 41. m1 and m5 y = -3x + 650, b. Which is different? When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles Answer: Perpendicular lines intersect at each other at right angles Answer: Question 8. The coordinates of the line of the second equation are: (-4, 0), and (0, 2) It is given that 8x 4x = 24 = 2.23 2 and 3 are the consecutive interior angles For a parallel line, there will be no intersecting point If the slope of two given lines are negative reciprocals of each other, they are identified as ______ lines. 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 ? Which rays are parallel? Then, according to the parallel line axiom, there is a different line than L2 that passes through the intersection point of L2 and L3 (point A in the drawing), which is parallel to L1. Compare the given coordinates with Hence, It also shows that a and b are cut by a transversal and they have the same length The missing information the student assuming from the diagram is: From the given figure, According to the Perpendicular Transversal theorem, We can conclude that quadrilateral JKLM is a square. For perpediclar lines, 2x + y = 162(1) Answer: Question 23.
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