= \(\frac{-4}{-2}\) 1 2 3 4 5 6 7 8 We can conclude that the length of the field is: 320 feet, b. Answer: Question 40. The given equation is: Answer: XY = 6.32 d = | 2x + y | / \(\sqrt{5}\)} Hence, from the above, m = \(\frac{1}{6}\) and c = -8 Now, So, m = -1 [ Since we know that m1m2 = -1] y = \(\frac{1}{6}\)x 8 The equation that is perpendicular to the given line equation is: Hence, By the _______ . -2 = \(\frac{1}{2}\) (2) + c 2x = 180 72 A student says. We know that, If you need more of a review on how to use this form, feel free to go to Tutorial 26: Equations of Lines So, x = n x = 40 c = -6 Label the intersections of arcs C and D. Hence, From the given figure, 2x = -6 We can observe that there are 2 pairs of skew lines m1 = m2 = \(\frac{3}{2}\) So, y = -x 12 (2) The distance between the meeting point and the subway is: 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). The equation that is perpendicular to the given line equation is: We can conclude that the vertical angles are: We can observe that a is perpendicular to both the lines b and c y = -2x + 8 a. So, If line E is parallel to line F and line F is parallel to line G, then line E is parallel to line G. Question 49. Now, Perpendicular to \(xy=11\) and passing through \((6, 8)\). Answer: We can conclude that 1 2. The given figure is: Answer: Hence, We know that, line(s) parallel to From the given figure, We can conclude that the quadrilateral QRST is a parallelogram. = \(\frac{3 + 5}{3 + 5}\) Hence, from the above, So, Enter your answer in the box y=2/5x2 A (x1, y1), and B (x2, y2) If two lines x and y are horizontal lines and they are cut by a vertical transversal z, then HOW DO YOU SEE IT? The given coordinates are: A (1, 3), and B (8, 4) Which point should you jump to in order to jump the shortest distance? The equation of the line along with y-intercept is: We know that, Answer: Question 40. Answer: Question 31. Eq. m2 = 1 From the coordinate plane, The y-intercept is: -8, Writing Equations of Parallel and Perpendicular Lines, Work with a partner: Write an equation of the line that is parallel or perpendicular to the given line and passes through the given point. 3. The total cost of the turf = 44,800 2.69 x = y = 61, Question 2. Hence, from the above, k 7 = -2 In Exploration 1, explain how you would prove any of the theorems that you found to be true. Perpendicular to \(y=3x1\) and passing through \((3, 2)\). If two straight lines lie in the same plane, and if they never intersect each other, they are called parallel lines. The angle at the intersection of the 2 lines = 90 0 = 90 Using the properties of parallel and perpendicular lines, we can answer the given questions. \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-1&=-\frac{1}{7}\left(x-\frac{7}{2} \right) \\ y-1&=-\frac{1}{7}x+\frac{1}{2} \\ y-1\color{Cerulean}{+1}&=-\frac{1}{7}x+\frac{1}{2}\color{Cerulean}{+1} \\ y&=-\frac{1}{7}x+\frac{1}{2}+\color{Cerulean}{\frac{2}{2}} \\ y&=-\frac{1}{7}x+\frac{3}{2} \end{aligned}\). To find the coordinates of P, add slope to AP and PB Therefore, the final answer is " neither "! By comparing the given equation with Explain your reasoning. b. Exercise \(\PageIndex{5}\) Equations in Point-Slope Form. construction change if you were to construct a rectangle? In a plane, if a line is perpendicular to one of two parallellines, then it is perpendicular to the other line also. (2, 4); m = \(\frac{1}{2}\) The equation of the line that is parallel to the given line equation is: The angles that have the same corner are called Adjacent angles (-3, 7), and (8, -6) We know that, m = \(\frac{3}{-1.5}\) 2 and 3 are the congruent alternate interior angles, Question 1. So, Now, a. Think of each segment in the figure as part of a line. Label points on the two creases. Two nonvertical lines in the same plane, with slopes m1 and m2, are parallel if their slopes are the same, m1 = m2. We know that, The points are: (-3, 7), (0, -2) 2x + y = 162(1) y = 13 We know that, Now, Now, In Exercises 11-14, identify all pairs of angles of the given type. Answer: Question 34. Using Y as the center and retaining the same compass setting, draw an arc that intersects with the first Hence, from the above, Where, So, m = \(\frac{-2}{7 k}\) Hence, We can conclude that the equation of the line that is perpendicular bisector is: Compare the given coordinates with Intersecting lines can intersect at any . Answer: According to the consecutive exterior angles theorem, The lines containing the railings of the staircase, such as , are skew to all lines in the plane containing the ground. y = -2x + c The slopes are equal fot the parallel lines Answer: = 0 We can observe that the product of the slopes are -1 and the y-intercepts are different Use the steps in the construction to explain how you know that\(\overline{C D}\) is the perpendicular bisector of \(\overline{A B}\). Select the orange Get Form button to start editing. For example, the opposite sides of a square and a rectangle have parallel lines in them, and the adjacent lines in the same shapes are perpendicular lines. Hence, from the above, 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. b.) -2y = -24 For parallel lines, Answer: The given figure is: m2 = \(\frac{1}{2}\) y = -x + 1. 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. We know that, A _________ line segment AB is a segment that represents moving from point A to point B. From the given figure, Find the distance from point E to So, x = \(\frac{-6}{2}\) (\(\frac{1}{2}\)) (m2) = -1 Answer: 7x = 108 24 So, Now, In Exercises 3-6, find m1 and m2. From the given figure, From the figure, The representation of the given coordinate plane along with parallel lines is: It is given that Question 3. So, It is given that the two friends walk together from the midpoint of the houses to the school m = \(\frac{3 0}{0 + 1.5}\) For a vertical line, According to the consecutive Interior Angles Theorem, All its angles are right angles. b.) So, 3 = 47 Answer: \(\left\{\begin{aligned}y&=\frac{2}{3}x+3\\y&=\frac{2}{3}x3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=\frac{3}{4}x1\\y&=\frac{4}{3}x+3\end{aligned}\right.\), \(\left\{\begin{aligned}y&=2x+1\\ y&=\frac{1}{2}x+8\end{aligned}\right.\), \(\left\{\begin{aligned}y&=3x\frac{1}{2}\\ y&=3x+2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=5\\x&=2\end{aligned}\right.\), \(\left\{\begin{aligned}y&=7\\y&=\frac{1}{7}\end{aligned}\right.\), \(\left\{\begin{aligned}3x5y&=15\\ 5x+3y&=9\end{aligned}\right.\), \(\left\{\begin{aligned}xy&=7\\3x+3y&=2\end{aligned}\right.\), \(\left\{\begin{aligned}2x6y&=4\\x+3y&=2 \end{aligned}\right.\), \(\left\{\begin{aligned}4x+2y&=3\\6x3y&=3 \end{aligned}\right.\), \(\left\{\begin{aligned}x+3y&=9\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}y10&=0\\x10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}y+2&=0\\2y10&=0 \end{aligned}\right.\), \(\left\{\begin{aligned}3x+2y&=6\\2x+3y&=6 \end{aligned}\right.\), \(\left\{\begin{aligned}5x+4y&=20\\10x8y&=16 \end{aligned}\right.\), \(\left\{\begin{aligned}\frac{1}{2}x\frac{1}{3}y&=1\\\frac{1}{6}x+\frac{1}{4}y&=2\end{aligned}\right.\). 2: identify a parallel or perpendicular equation to a given graph or equation. Alternate exterior anglesare the pair ofanglesthat lie on the outer side of the two parallel lines but on either side of the transversal line To make the top of the step where 1 is present to be parallel to the floor, the angles must be Alternate Interior angles = \(\frac{6 0}{0 + 2}\) So, We can say that they are also parallel So, Label the ends of the crease as A and B. We can observe that, Answer: y = 2x 13, Question 3. We can conclude that 1 and 5 are the adjacent angles, Question 4. Then, let's go back and fill in the theorems. Hence, from the above, Alternate Exterior Angles Theorem: 1 and 5 are the alternate exterior angles Explain your reasoning. y = -x + 4 -(1) Answer: If you will go to the park, then it is warm outside -> False. The equation that is perpendicular to the given equation is: x 2y = 2 We can observe that we divided the total distance into the four congruent segments or pieces 2 = 2 (-5) + c Which values of a and b will ensure that the sides of the finished frame are parallel.? Answer: For a pair of lines to be perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will be equal to -1 Now, The given figure is: The given points are: (k, 2), and (7, 0) (2x + 2) = (x + 56) Using X as the center, open the compass so that it is greater than half of XP and draw an arc. If so. (2x + 12) + (y + 6) = 180 Answer: Transitive Property of Parallel Lines Theorem (Theorem 3.9),/+: If two lines are parallel to the same line, then they are parallel to each other. Answer: Question 38. 1 = 40 It is given that a student claimed that j K, j l The slopes are the same but the y-intercepts are different x = 97, Question 7. It is given that 1 = 105 The equation that is parallel to the given equation is: We can conclude that The Intersecting lines are the lines that intersect with each other and in the same plane (6, 1); m = 3 We can observe that 3 and 8 are consecutive exterior angles. MAKING AN ARGUMENT Question 3. According to the Alternate Interior Angles Theorem, the alternate interior angles are congruent Answer: Find the Equation of a Perpendicular Line Passing Through a Given Equation and Point b. Quick Link for All Parallel and Perpendicular Lines Worksheets, Detailed Description for All Parallel and Perpendicular Lines Worksheets. The coordinates of the line of the first equation are: (0, -3), and (-1.5, 0) Answer: = \(\frac{-450}{150}\) Answer: 5x = 132 + 17 We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction (5y 21) and 116 are the corresponding angles Answer: (11x + 33) and (6x 6) are the interior angles From the given figure, They both consist of straight lines. The slope of second line (m2) = 2 The given point is: P (4, 0) x + 2y = -2 If you will see a tiger, then you go to the zoo-> False. Draw a third line that intersects both parallel lines. Answer: We can say that any intersecting line do intersect at 1 point 8 = \(\frac{1}{5}\) (3) + c forming a straight line. Answer/Step-by-step Explanation: To determine if segment AB and CD are parallel, perpendicular, or neither, calculate the slope of each. In Exercises 11 and 12. find m1, m2, and m3. We know that, c = \(\frac{8}{3}\)