Test Corrections for Unit 1 Test


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1 MUST READ DIRECTIONS: Read the directions located on to understand how to properly do test corrections. Ask for clarification from your teacher if there are parts that you are unclear about. Any test corrections submitted without meeting all the requirements of the test corrections format will not be accepted/scored. Any test corrections submitted past the due date will not be accepted/scored. Test corrections are a privilege, not a right. The goal is for you to remediate your skills, apply them to new problems and be able to fully and accurately explain the how and why of each problem. These test corrections take a long time to complete, however, they can earn you up to 1/2 of the points back that you lost on the Unit 1 test. If you take advantage of this opportunity you will not only understand the material better, but you will also improve your grade in the class. 1. Trapezoid ABCD has coordinates A(0,9), B(12,9), C(8,4), and D(0,4). a) Using coordinate geometry, show that AD is not parallel to BC. 5. In the diagram below, quadrilateral ABCD has vertices A( 5,1), B(6, 1), C(3,5), and D( 2,7). b) Find the area of trapezoid ABCD. c) Find the perimeter of ABCD to the nearest integer. d) Find m ABC to the nearest degree. 2. Point P has coordinates ( 12,5). What is its distance from the origin? 3. Find an equation of the line passing through the point (6,5) and perpendicular to the line whose equation is 2y+3x = Square ABCD has vertices A( 2, 3), B(4, 1), C(2,5), and D( 4,3). What is the length of a side of the square? A. 2 5 B C. 4 5 D What are the coordinates of the midpoint of diagonal AC? A. ( 1,3) B. (1,3) C. (1,4) D. (2,3) 6. Find the distance between the points ( 1, 5) and ( 7,3). page 1
2 7. Line l passes through the point (5,3) and is parallel to line k whose equation is 5x+y = 6. An equation of line l is A. y = 1 5x+2 B. y = 5x+28 C. y = 1 5x 2 D. y = 5x In the coordinate plane, the points (2,2) and (2,12) are the endpoints of a diameter of a circle. What is the length of the radius of the circle? A. 5 B. 6 C. 7 D What is an equation of the line that passes through the point (7,3) and is parallel to the line 4x+2y = 10? A. y = 1 2 x 1 2 B. y = 1 2 x C. y = 2x 11 D. y = 2x What is the length of the line segment joining the points ( 3, 4) and (2, 5)? 14. Trapezoid ABCD has coordinates A( 6,0), B(17,0), C(2,8), and D(0,8). Find the a) area of trapezoid ABCD b) perimeter of trapezoid ABCD c) measure of B to the nearest degree 15. The midpoint of AB is M, the coordinates of A are (a,b), and the coordinates of B are (a+4,5b). What are the coordinates of M? A. (2,2b) B. (a+2,3b) C. (2a+4,6b) D. ( a+4 2, 5b ) Triangle HKL has vertices H( 7, 2), K(3, 4), and L(5,4). The midpoint of HL is M and the midpoint of LK is N. Determine and state the coordinates of points M and N. Justify the statement: MN is parallel to HK. [The use of the set of axes below is optional.] 11. In parallelogram ABCD, the coordinates of A are (4,3) and the coordinates of the midpoint of diagonal AC are (2,5). What are the coordinates of C? 12. The coordinates of the endpoints of the diameter of a circle are (3,7) and ( 5,3). Find the coordinates of the center of the circle. 13. The coordinates of A and B are (2a,4b) and (8a, 6b), respectively. Express in terms of a and b, the coordinates of the midpoint of AB. page 2
3 17. The coordinates of the vertices of ABC are A( 4,1), B(4,9), C(9, 2). Point M(1,6) lies on AB. a) Show by means of coordinate geometry that CM AB. b) Find, to the nearest degree, the measure of angle A. 18. The graph of the equation y = 1 3 x + 2 is perpendicular to the graph of the equation A. y = 1 3x+5 B. 3y = x+2 C. y = 3x+5 D. y = 3x Which point is farthest from the origin? A. (0, 5) B. (6,0) C. (3,4) D. (4,2) 20. Triangle ABC has vertices A( 2, 1), B(5, 5), and C( 1, 7). a) Show that ABC is isosceles. b) Find the length of the altitude drawn from A to BC. c) Using the results obtained in parts a and b, find, to the nearest degree, the measure of a base angle of this triangle. 21. Which equation represents a line parallel to the line whose equation is 2y = 3x+6? A. 3y = 2x+6 B. 2y = 3x Which equation represents a line that is parallel to the line whose equation is 2x+3y = 12? A. 6y 4x = 2 B. 6y+4x = 2 C. 4x 6y = 2 D. 6x+4y = Segment AB is the diameter of a circle whose center is the point (2,5). If the coordinates of A are (1,3), find the coordinates of B. 24. Points A(5,3) and B(7,6) lie on AB. Points C(6,4) and D(9,0) lie on CD. Which statement is true? A. B. C. D. AB CD AB CD AB and CD are the same line. AB and CD intersect, but are not perpendicular. 25. Which equation represents a line that is parallel to the line whose equation is 3x 2y = 7? A. y = 3 2 x+5 B. y = 2 3 x+4 C. y = 3 2 x 5 D. y = 2 3 x Which line is perpendicular to the line whose equation is 5y+6 = 3x? A. y = 5 3 x+7 B. y = 5 3 x+7 C. y = 3 5 x+7 D. y = 3 5 x+7 C. y = 2 3 x+1 D. y = 3 2 x 4 page 3
4 27. Write an equation of the perpendicular bisector of the line segment whose endpoints are ( 1,1) and (7, 5). [The use of the grid below is optional.] 29. Write an equation of the line that passes through the point (6, 5) and is parallel to the line whose equation is 2x 3y = What is an equation of the line that passes through the point (3, 1) and has a slope of 2? A. y = 2x+5 B. y = 2x 1 C. y = 2x 4 D. y = 2x What is the equation of the line that is perpendicular to the line y 2x = 4 and passes through point (2, 4)? A. y = 1 2 x+4 B. y = 1 2 x+5 C. y = 1 2x+5 D. y = 2x Which equation represents the line that passes through the point (0,1) and is parallel to the line whose equation is 3x+y = 5? A. 3x+y = 3 B. 3x+y = 1 C. 3x+y = 0 D. 3x+y = 1! " # $ " % &! " #! # ' & ( ) * # + ), & !. ' & ( ) * # / 0 % & * # $! " * 1 page 4
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1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.
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