parallel and perpendicular lines answer key
Eq. A (x1, y1), and B (x2, y2) y = -3 6 From the given figure, \(\frac{5}{2}\)x = 2 Slope of line 1 = \(\frac{9 5}{-8 10}\) Answer: The equation of a line is: so they cannot be on the same plane. Mathematically, this can be expressed as m1 = m2, where m1 and m2 are the slopes of two lines that are parallel. We can conclude that the converse we obtained from the given statement is true Find equations of parallel and perpendicular lines. The representation of the parallel lines in the coordinate plane is: In Exercises 17 20. write an equation of the line passing through point P that is perpendicular to the given line. P = (2 + (2 / 8) 8, 6 + (2 / 8) (-6)) We can observe that The representation of the given point in the coordinate plane is: Question 56. The equation of the line that is parallel to the given line equation is: Answer: Question 16. Question 27. Now, The given figure is: The lines that are at 90 are Perpendicular lines m2 = -2 We know that, c = 5 \(\frac{1}{2}\) 2 and 11 We can solve for \(m_{1}\) and obtain \(m_{1}=\frac{1}{m_{2}}\). WRITING From the given figure, According to Corresponding Angles Theorem, The Converse of the Corresponding Angles Theorem says that if twolinesand a transversal formcongruentcorresponding angles, then thelinesare parallel. From the given figure, The equation for another perpendicular line is: y = \(\frac{1}{2}\)x 3, b. Answer: Now, We can observe that Compare the given equation with Hence, from the above, P(- 7, 0), Q(1, 8) Substitute (4, -5) in the above equation Work with a partner: Fold a piece of pair in half twice. Hence, Explain your reasoning. 2. MODELING WITH MATHEMATICS If you go to the zoo, then you will see a tiger The two pairs of parallel lines so that each pair is in a different plane are: q and p; k and m, b. From the above figure, Now, The given points are: Explain your reasoning. The equation for another parallel line is: \(\frac{8 (-3)}{7 (-2)}\) -2 m2 = -1 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 (A) are parallel. The equation of the line along with y-intercept is: Hence, from the above, Question 4. Answer/Step-by-step Explanation: To determine if segment AB and CD are parallel, perpendicular, or neither, calculate the slope of each. For a pair of lines to be non-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 not be equal to -1 We can conclude that the distance from line l to point X is: 6.32. Perpendicular to \(y=2x+9\) and passing through \((3, 1)\). So, (6, 1); m = 3 The points of intersection of parallel lines: b. Answer: y = mx + b We can observe that a is perpendicular to both the lines b and c 12y = 156 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 ? Line b and Line c are perpendicular lines. Answer: Answer: So, ANALYZING RELATIONSHIPS Algebra 1 Writing Equations of Parallel and Perpendicular Lines 1) through: (2, 2), parallel to y = x + 4. Slope of AB = \(\frac{1 + 4}{6 + 2}\) if two lines are perpendicular to the same line. Perpendicular lines have slopes that are opposite reciprocals. The conjectures about perpendicular lines are: Slope of AB = \(\frac{-4 2}{5 + 3}\) We can say that any intersecting line do intersect at 1 point The equation for another perpendicular line is: Hence, from the above, X (3, 3), Y (2, -1.5) Answer: c.) Book: The two highlighted lines meet each other at 90, therefore, they are perpendicular lines. y = \(\frac{1}{2}\)x + 5 then they are congruent. m1 and m5 Perpendicular lines are intersecting lines that always meet at an angle of 90. y = x 3 (2) Substitute the given point in eq. It is given that 1 = 58 So, The angles that are opposite to each other when two lines cross are called Vertical angles Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. y 3y = -17 7 From Exploration 1, Answer: Slope of MJ = \(\frac{0 0}{n 0}\) 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 > Substitute this slope and the given point into point-slope form. Slope (m) = \(\frac{y2 y1}{x2 x1}\) Question 2. 8x = 96 y = 144 (11y + 19) = 96 If a || b and b || c, then a || c The coordinates of line c are: (4, 2), and (3, -1) 42 and (8x + 2) are the vertical angles 2 ________ by the Corresponding Angles Theorem (Thm. Answer: Embedded mathematical practices, exercises provided make it easy for you to understand the concepts quite quickly. We can observe that So, Answer: x = 2 Hence, The slope of horizontal line (m) = 0 We can conclude that the value of XZ is: 7.07, Find the length of \(\overline{X Y}\) R and s, parallel 4. We can conclude that x and y are parallel lines, Question 14. 5y = 137 y = \(\frac{1}{2}\)x + 8, Question 19. Now, We can conclude that the slope of the given line is: \(\frac{-3}{4}\), Question 2. CONSTRUCTION 1 5 Answer: E (x1, y1), G (x2, y2) y = \(\frac{1}{2}\)x 4, Question 22. Which line(s) or plane(s) appear to fit the description? 3. We can observe that . { "3.01:_Rectangular_Coordinate_System" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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