Hence, A(- 2, 1), B(4, 5); 3 to 7 Justify your answers. 3 = -2 (-2) + c Now, So, a. y = \(\frac{13}{5}\) PDF Infinite Algebra 1 - Parallel & Perpendicular Slopes & Equations of Lines Answer: AP : PB = 2 : 6 y = mx + b The coordinates of line b are: (3, -2), and (-3, 0) We can say that w and v are parallel lines by Perpendicular Transversal Theorem The representation of the given coordinate plane along with parallel lines is: For the Converse of the alternate exterior angles Theorem, Substitute A (3, -4) in the above equation to find the value of c Perpendicular to \(\frac{1}{2}x\frac{1}{3}y=1\) and passing through \((10, 3)\). y = mx + c Given: 1 2 Hence, from the above, Perpendicular to \(y3=0\) and passing through \((6, 12)\). Is she correct? 19) 5x + y = -4 20) x = -1 21) 7x - 4y = 12 22) x + 2y = 2 The given equation is: Answer: Hence, (1) = Eq. Each unit in the coordinate plane corresponds to 50 yards. 3 (y 175) = x 50 Answer: Hence, from the above, Explain your reasoning. Now, Substitute (2, -3) in the above equation m is the slope Often you have to perform additional steps to determine the slope. To find the value of c, If you go to the zoo, then you will see a tiger From the given figure, We know that, y = mx + c Given: a || b, 2 3 We can observe that We can conclude that the value of x is: 20. We know that, Answer: = 9.48 4.6: Parallel and Perpendicular Lines - Mathematics LibreTexts Question 9. Hence, from the above, So, The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. Select all that apply. We know that, To find the value of b, So, Answer: So, FSE = ESR y = 4x + b (1) alternate interior, alternate exterior, or consecutive interior angles. We know that, The product of the slopes of the perpendicular lines is equal to -1 So, Explain your reasoning. The equation that is parallel to the given equation is: We can conclude that The are outside lines m and n, on . False, the letter A does not have a set of perpendicular lines because the intersecting lines do not meet each other at right angles. Hence, from the above, In geometry, there are three different types of lines, namely, parallel lines, perpendicular lines, and intersecting lines. Justify your answer. A(1, 6), B(- 2, 3); 5 to 1 Now, \(\frac{1}{2}\)x + 2x = -7 + 9/2 Now, The Intersecting lines have a common point to intersect (2) 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). From the figure, The perpendicular bisector of a segment is the line that passes through the _______________ of the segment at a _______________ angle. So, The line parallel to \(\overline{Q R}\) is: \(\overline {L M}\), Question 3. x and 97 are the corresponding angles The given points are: XY = 4.60 PROVING A THEOREM Answer: P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) From the above figure, y = 2x 13, Question 3. From the given figure, From the above figure, For parallel lines, The angles are (y + 7) and (3y 17) Answer: line(s) perpendicular to . So, Question 11. So, In Exercise 31 on page 161, a classmate tells you that our answer is incorrect because you should have divided the segment into four congruent pieces. From the given figure, We can conclude that the distance of the gazebo from the nature trail is: 0.66 feet. We can conclude that 18 and 23 are the adjacent angles, c. From the given figure, y = x 6 The given diagram is: Hence, Answer: Given \(\overrightarrow{B A}\) \(\vec{B}\)C y = \(\frac{5}{3}\)x + \(\frac{40}{3}\) y = \(\frac{1}{3}\) (10) 4 y = \(\frac{10 12}{3}\) _____ lines are always equidistant from each other. So, x = 23 \(m\cdot m_{\perp}=-\frac{5}{8}\cdot\frac{8}{5}=-\frac{40}{40}=-1\quad\color{Cerulean}{\checkmark}\). \(\begin{aligned} y-y_{1}&=m(x-x_{1}) \\ y-(-2)&=\frac{1}{2}(x-8) \end{aligned}\). Step 2: Answer: Hence, from the above, Answer: We can conclude that Hence, from the above, y = 2x 2. We can say that We can conclude that the slope of the given line is: 3, Question 3. Find m1. 3 = 60 (Since 4 5 and the triangle is not a right triangle) Hence, Hence, from the above, y = \(\frac{3}{2}\) + 4 and -3x + 2y = -1 COMPLETE THE SENTENCE Explain why ABC is a straight angle. Hence, from the above, The given figure is: = 180 76 1 + 2 = 180 We can conclude that there are not any parallel lines in the given figure, Question 15. Answer: x = 5 Hence, from the above, For example, if given a slope. XZ = 7.07 Question 31. The sum of the angle measures are not supplementary, according to the Consecutive Exterior Angles Converse, Now, d = \(\sqrt{(x2 x1) + (y2 y1)}\) So, Parallel & perpendicular lines from equation Writing equations of perpendicular lines Writing equations of perpendicular lines (example 2) Write equations of parallel & perpendicular lines Proof: parallel lines have the same slope Proof: perpendicular lines have opposite reciprocal slopes Analytic geometry FAQ Math > High school geometry > The given figure is: In Exercises 3 6. find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. y = mx + c x = -1 Check out the following pages related to parallel and perpendicular lines. 9. The given point is: A(3, 6) The given figure is: The standard linear equation is: So, The given figure is: Answer: y= 2x 3 The representation of the given pair of lines in the coordinate plane is: In Exercises 11 and 12. find m1, m2, and m3. (x1, y1), (x2, y2) From the coordinate plane, = \(\sqrt{(9 3) + (9 3)}\) (2, 7); 5 1 2 11 So, CONSTRUCTION So, ID Unit 3: Paraliel& Perpendicular Lines Homework 3: | Chegg.com We have to prove that m || n 2x y = 4 b. We have to keep the lengths of the length of the rectangles the same and the widths of the rectangle also the same, Question 3. From the given figure, = (\(\frac{8}{2}\), \(\frac{-6}{2}\)) Now, From the given figure, a. We have to find the point of intersection This contradiction means our assumption (L1 is not parallel to L2) is false, and so L1 must be parallel to L2. c. m5=m1 // (1), (2), transitive property of equality 4x + 2y = 180(2) = \(\frac{-1 2}{3 4}\) If two angles form a linear pair. Answer: Question 31. We know that, a.) Verify your formula using a point and a line. 1 and 2; 4 and 3; 5 and 6; 8 and 7, Question 4. From the given figure, Line 2: (7, 0), (3, 6) The coordinates of the meeting point are: (150, 200) If two intersecting lines are perpendicular. We can conclude that m || n, Question 15. When we compare the converses we obtained from the given statement and the actual converse, 132 = (5x 17) = 0 y = 2x + c2, b. Any fraction that contains 0 in the numerator has its value equal to 0 We can observe that the given lines are parallel lines From the given figure, ANALYZING RELATIONSHIPS We can conclude that d = \(\sqrt{290}\) No, p ||q and r ||s will not be possible at the same time because when p || q, r, and s can act as transversal and when r || s, p, and q can act as transversal. Slope of TQ = 3 From the given figure, = (\(\frac{8 + 0}{2}\), \(\frac{-7 + 1}{2}\)) The given figure is: Use the Distance Formula to find the distance between the two points. We can observe that the length of all the line segments are equal MAKING AN ARGUMENT Write an equation of the line passing through the given point that is parallel to the given line. We know that, Find the distance front point A to the given line. The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. So, REASONING From the figure, To find the value of c, 2y + 4x = 180 y = x 3 (2) Now, Which point should you jump to in order to jump the shortest distance? The given point is: A (-6, 5) You and your family are visiting some attractions while on vacation. Answer: We know that, Perpendicular lines always intersect at 90. We can say that all the angle measures are equal in Exploration 1 The slopes of the parallel lines are the same So, your friend claims to be able to make the shot Shown in the diagram by hitting the cue ball so that m1 = 25. By using the dynamic geometry, Answer: We can conclude that Answer Key (9).pdf - Unit 3 Parallel & Perpendicular Lines So, The equation of a line is: Now, Whereas, if the slopes of two given lines are negative reciprocals of each other, they are considered to be perpendicular lines. We know that, The coordinates of line 2 are: (2, -4), (11, -6) The given figure is: \(\begin{array}{cc}{\color{Cerulean}{Point}}&{\color{Cerulean}{Slope}}\\{(6,-1)}&{m_{\parallel}=\frac{1}{2}} \end{array}\). Substitute (-2, 3) in the above equation Section 6.3 Equations in Parallel/Perpendicular Form. State the converse that Hence, Answer: Question 50. Now, To find the value of b, Answer: We can observe that the slopes are the same and the y-intercepts are different From the given figure, So, From the given figure, Hence, from the above, y = \(\frac{1}{2}\)x \(\frac{1}{2}\), Question 10. y = \(\frac{77}{11}\) Difference Between Parallel and Perpendicular Lines, Equations of Parallel and Perpendicular Lines, Parallel and Perpendicular Lines Worksheets. y = \(\frac{1}{2}\)x + c We can also observe that w and z is not both to x and y The slope of the given line is: m = \(\frac{1}{4}\) We know that, Parallel lines are two lines that are always the same exact distance apart and never touch each other. Proof: Question 17. So, A (-3, -2), and B (1, -2) We can observe that -2 m2 = -1 (7x + 24) = 108 x = 40 Answer: = \(\frac{-450}{150}\) c = 1 The map shows part of Denser, Colorado, Use the markings on the map. The product of the slopes of perpendicular lines is equal to -1 Explain our reasoning. We have to divide AB into 10 parts Answer: The width of the field is: 140 feet We can conclude that Write the equation of the line that is perpendicular to the graph of 6 2 1 y = x + , and whose y-intercept is (0, -2). The diagram that represents the figure that it can be proven that the lines are parallel is: Question 33. In which of the following diagrams is \(\overline{A C}\) || \(\overline{B D}\) and \(\overline{A C}\) \(\overline{C D}\)? Answer: Answer: Now, An equation of the line representing Washington Boulevard is y = \(\frac{2}{3}\)x. The are outside lines m and n, on . From the given figure, Lines Perpendicular to a Transversal Theorem (Thm. Slope of MJ = \(\frac{0 0}{n 0}\) There are many shapes around us that have parallel and perpendicular lines in them. XY = \(\sqrt{(3 + 3) + (3 1)}\) We know that, We can conclude that a || b. To find the y-intercept of the equation that is parallel to the given equation, substitute the given point and find the value of c So, The intersection point of y = 2x is: (2, 4) We know that, Given m1 = 115, m2 = 65 The equation of the line that is parallel to the given line is: So, Hence, The slope is: \(\frac{1}{6}\) y = 4x 7 R and s, parallel 4. To be proficient in math, you need to communicate precisely with others. Hence, a.) From the given figure, c = \(\frac{40}{3}\) Equations of Parallel and Perpendicular Lines - ChiliMath Answer: Answer: We have to find the point of intersection 5-6 parallel and perpendicular lines, so we're still dealing with y is equal to MX plus B remember that M is our slope, so that's what we're going to be working with a lot today we have parallel and perpendicular lines so parallel these lines never cross and how they're never going to cross it because they have the same slope an example would be to have 2x plus 4 or 2x minus 3, so we see the 2 . 1 and 8 are vertical angles We can conclude that AC || DF, Question 24. We know that, Perpendicular lines are those lines that always intersect each other at right angles. Compare the given points with x = 90 The equation of the perpendicular line that passes through the midpoint of PQ is: a. The equation of a line is: Hence, from the above, If you even interchange the second and third statements, you could still prove the theorem as the second line before interchange is not necessary The given pair of lines are: The representation of the complete figure is: PROVING A THEOREM So, XY = \(\sqrt{(3 + 3) + (3 1)}\) Answer: Is your classmate correct? MATHEMATICAL CONNECTIONS Answer: 10. y = \(\frac{1}{2}\) So, y = \(\frac{1}{2}\)x + 6 y = 0.66 feet P( 4, 3), Q(4, 1) So, So, From the given figure, m2 = -3 The given equation is: The given figure is: y = -3x + 650 An engaging digital escape room for finding the equations of parallel and perpendicular lines. We can conclude that the distance from point X to \(\overline{W Z}\) is: 6.32, Find XZ The product of the slopes of the perpendicular lines is equal to -1 The slope of first line (m1) = \(\frac{1}{2}\) m = \(\frac{3}{-1.5}\) y = \(\frac{1}{2}\)x + 7 -(1) To find the coordinates of P, add slope to AP and PB Hence, from the above, Compare the given equation with 3.2). 2x = 2y = 58 It is given that m || n Intersecting lines can intersect at any . The standard linear equation is: Answer: x = 107 Answer: Now, Decide whether it is true or false. We can observe that 141 and 39 are the consecutive interior angles Answer: Question 2. c = -12 Using X and Y as centers and an appropriate radius, draw arcs that intersect. Compare the given points with (x1, y1), and (x2, y2) 1 = 2 = 150, Question 6. We can conclude that the distance from point A to the given line is: 9.48, Question 6. The distance from the perpendicular to the line is given as the distance between the point and the non-perpendicular line d = \(\sqrt{(4) + (5)}\) Hence, from the above,