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Name: ________________________ Class: ___________________ Date: __________ ID: A Parallel & Perpendicular Lines Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. What is the slope of a line perpendicular to the line whose equation is 5x + 3y = 8? 5 3 c. − a. 3 5 3 5 b. d. − 5 3 ____ 2. Which graph could be used to find the solution to the following system of equations? y = −x + 2 y=x ____ a. c. b. d. 2 3. What is the equation of a line that passes through the point (−3, −11) and is parallel to the line whose equation is 2x − y = 4? 1 25 a. y = 2x + 5 c. y = x + 2 2 1 25 b. y = 2x − 5 d. y = − x − 2 2 1 Name: ________________________ ____ ID: A ←→ ←→ 4. The diagram below illustrates the construction of PS parallel to RQ through point P. Which statement justifies this construction? c. PR ≅ RQ a. m∠1 = m∠2 b. m∠1 = m∠3 d. PS ≅ RQ ____ 5. Find m∠ABC . a. m∠ABC = 40º b. m∠ABC = 45º ____ c. m∠ABC = 35º d. m∠ABC = 50º 2 6. Given the system of equations: y = x − 4x x=4 The number of points of intersection is a. 1 b. 2 c. 3 d. 0 2 Name: ________________________ ____ ____ ID: A 2 7. What is the slope of a line perpendicular to the line whose equation is y = − x − 5? 3 3 2 a. − c. 2 3 2 3 b. − d. 3 2 8. The two lines represented by the equations below are graphed on a coordinate plane. x + 6y = 12 3(x − 2) = −y − 4 Which statement best describes the two lines? a. The lines are parallel. b. The lines are the same line. c. The lines are perpendicular. d. The lines intersect at an angle other than 90°. ____ ____ 9. A transversal intersects two lines. Which condition would always make the two lines parallel? a. Vertical angles are congruent. b. Alternate interior angles are congruent. c. Corresponding angles are supplementary. d. Same-side interior angles are complementary. 10. Find the slope of the line that contains (5, − 6) and (−1, − 4). a. 2 c. 5 d. −3 −5 b. − 2 ____ 1 −3 11. Based on the diagram below, which statement is true? a. a Ä b b. a Ä c c. b Ä c d. d Ä e 3 Name: ________________________ ID: A Short Answer 12. Find an equation of the line passing through the point (5, 4) and parallel to the line whose equation is 2x + y = 3. Answer:_________________________________ 13. Solve the following system of equations graphically. 2 2x − 4x = y + 1 x+y=1 4 ID: A Parallel & Perpendicular Lines Unit Review Answer Section MULTIPLE CHOICE 1. ANS: B A 5 so the slope of this line is − Perpendicular lines have B 3 slope that are the opposite and reciprocal of each other. The slope of a line in standard form is − PTS: 2 REF: fall0828ge TOP: Parallel and Perpendicular Lines 2. ANS: C STA: G.G.62 PTS: 2 REF: fall0805ge TOP: Quadratic-Linear Systems 3. ANS: B STA: G.G.70 A −2 = 2. A parallel line The slope of a line in standard form is − , so the slope of this line is B −1 would also have a slope of 2. Since the answers are in slope intercept form, find the y-intercept: y = mx + b −11 = 2(−3) + b −5 = b PTS: TOP: 4. ANS: TOP: 2 REF: fall0812ge Parallel and Perpendicular Lines A PTS: 2 Constructions STA: G.G.65 REF: fall0807ge 1 STA: G.G.19 ID: A 5. ANS: C (x)° = (3x − 70)° 0 = 2x − 70 70 = 2x 35 = x m∠ABC = 3x − 70 m∠ABC = 3(35) − 70 = 35° Corresponding angles are congruent. Subtract x from both sides. Add 70 to both sides. Divide both sides by 2. Substitute 35 for x. Simplify. Feedback A B C D If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Use the Corresponding Angles Postulate. Correct! First, set the measures of the corresponding angles equal to each other. Then, solve for x and substitute in the expression (3x - 70). PTS: 1 DIF: Advanced NAT: 8.3.3.g TOP: 7-2 Parallel and Perpendicular Lines 6. ANS: A STA: 8.G.4 2 2 y = x − 4x = (4) − 4(4) = 0. (4, 0) is the only intersection. PTS: 2 REF: 060923ge STA: G.G.70 TOP: Quadratic-Linear Systems 7. ANS: D 2 2 The slope of y = − x − 5 is − . Perpendicular lines have slope that are opposite reciprocals. 3 3 PTS: 2 REF: 080917ge TOP: Parallel and Perpendicular Lines STA: G.G.62 2 ID: A 8. ANS: D x + 6y = 12 6y = −x + 12 1 y= − x+2 6 m=− 3(x − 2) = −y − 4 −3(x − 2) = y + 4 m = −3 1 6 PTS: 2 REF: 011119ge STA: TOP: Parallel and Perpendicular Lines 9. ANS: B PTS: 2 REF: TOP: Parallel Lines and Transversals 10. ANS: C y2 − y1 Use the slope formula. m= x2 − x1 (−4) − (−6) Substitute (5, − 6) for (x 1 , m= (−1) − (5) 2 1 Simplify. m= = −3 −6 G.G.63 061007ge STA: G.G.35 y 1 ) and (−1, − 4) for (x 2 , y 2 ). Feedback A B C D Divide the difference in y-values by the difference in x-values. First, substitute the coordinates of the first point into (x1, x2) and the coordinates of the second point into (y1, y2) of the slope formula. Then, simplify. Correct! Use the slope formula. PTS: 1 DIF: Basic REF: Page 320 OBJ: 5-4.1 Finding Slope by Using the Slope Formula NAT: 12.5.2.b STA: A.A.33 TOP: 5-4 The Slope Formula 11. ANS: D The marked 60º angle and the angle above it are on the same straight line and supplementary. This unmarked supplementary angle is 120º. Because the unmarked 120º angle and the marked 120º angle are alternate exterior angles and congruent, d Ä e. PTS: 2 REF: 080901ge TOP: Parallel Lines and Transversals STA: G.G.35 3 ID: A SHORT ANSWER 12. ANS: y = −2x + 14. The slope of 2x + y = 3 is −A −2 = = −2. y = mx + b . 1 B 4 = (−2)(5) + b b = 14 PTS: 2 REF: 060931ge TOP: Parallel and Perpendicular Lines 13. ANS: STA: G.G.65 PTS: 4 REF: 061137ge TOP: Quadratic-Linear Systems STA: G.G.70 4