Constructions & Transformations

1. Constructions&Transformations Review Problems

2. #1 • If two lines lie in the same plane and do NOT intersect, they are called _______. A. bisectors B. horizontal C. parallel D. perpendicular

3. #2 • If is reflected across the x-axis, what are the resulting coordinates of point B? A. (3, 1) B. (-3, 1) C. (-3, -1) D. (3, -1)

4. #3 • A model of a house has been drawn on a coordinate grid. One corner of the house has been drawn at (1, 5). The drawing will be translated two units up and three units to the right. Where will the same corner of the house be after the translation? A. (-2, 3) B. (-1, 2) C. (3, 8) D. (4, 7)

5. #4 • A point was graphed at (-3, 3). The point was translated to (3, 3) and then translated to (3, -3). Which translations occurred. A. two equal dilations B. reflection over the x-axis, then a rotation C. reflection over the y-axis, then a reflection over the x-axis. D. reflection over the x-axis, then a reflection over the y-axis

6. #5 • For the construction shown, which of the following arcs must be drawn first? A. 1 B. 2 C. 3 D. 4

7. #6 • The diagram shows a geometric figure on a coordinate plane. • Which diagram shows a rotation of the geometric figure?

8. #7 The drawing shows a compass and straightedge construction of – A. a perpendicular to a given line from a point not on the line B. a perpendicular to a given line at a point on the line C. the bisector of a given angle D. an angle congruent to a given angle

9. #8 • In a chess game, a knight’s move is 2 units in one direction and 1 unit in a perpendicular direction. If a knight starts at the origin and makes one move, which could NOT be its location? A. (-1, -2) B. (1, 2) C. (2, -1) D. (-2, 2)

10. #9 • Joan wants to bisect . What should she do first? A. Swing an arc from point F B. Swing an arc from point G. C. Swing an arc from point H D. Use her straightedge to draw a segment.

11. #10 • To bisect , John began by swinging equal arcs from points P and Q above the segment and labeling point X where the arcs met. What should John do next? A. Use a straightedge to draw a line segment from X to P and a line segment from X to Q. B. Use a straightedge to draw a line segment from X to the point in the middle of C. Swing an arc from point X. D. Swing equal arcs from points P and Q below the segment.

12. #11 • A line segment has length of 36 cm. If Lu bisects the segment, what is the length of each segment he constructs? A. 12 cm B. 18 cm C. 36 cm D. 72 cm

13. #12 • Which set of transformations returns a given figure to its original location? A. translation 2 units left, then 3 units up, then 3 units right, then 2 units down B. reflection across the y-axis, then the x-axis, then the y-axis, and then the x-axis C. 180° counterclockwise rotation D. 90° clockwise rotation, then reflection across the line y = x

14. #13 • On a coordinate plane, point A has coordinates (-11, 3). Point A’ is the result of reflecting point A across the x-axis. What are the coordinates of point A’? • (-11, -3) • (11, -3) • (11, 3) • (3, -11)

15. #14 • Which figure shows a rotation? A. B. C. D.

16. #15 • Which figure shows a translation? A. B. C. D.

17. #16 • Which figure shows a reflection? A. B. C. D.

18. #17 • To bisect an angle means to ______ • Copy it • Cut it in half • Double its size • Rotate it

19. #18 • The midpoint of line segment ST is point K. If line segment SK equals 13.5 meters, how long is line segment ST? • 13.5 m • 26 m • 27 m • 28 m

20. #19 • Which statement is true? • An angle bisector is one of the sides of a given angle. • An angle bisector is outside the given angle. • An angle bisector divides a given angle into two angles with the same measure. • An angle bisector is outside the plane containing a given angle.

21. #20 • Nora is copying angle D. She has drawn ray BG, and then drawn an arc through angle D. What should she do next? • Use the same compass setting to draw an arc through ray BG. • Use the same compass opening to measure the opening of angle D. • Change the compass opening to draw an arc through ray BG. • Draw ray BD.

22. #21 • Leo was given point M and line GH. Point M is not on line GH. How many lines can he construct parallel to GH through M? • 0 • 1 • 2 • An infinite number

23. #22 (challenge) • Linda was told to construct a square. She drew line CD. Then she constructed line AB parallel to line CD through point A. What should she do next? • Construct a line perpendicular to AB using any point on line CD • Construct a line parallel to AB using any point on line CD. • Draw line segment AC • Draw line segment AD

24. #23 What is being constructed in the diagram? • A line through point S parallel to line r • A line through point S not parallel to line r • A line through point S perpendicular to line r • A line through point S congruent to line r S B A r

25. #24 • A certain translation moves points 2 units to the right and 6 units down. What are the coordinates of B’, the image of point B (-4, 7) after this translation? • B’ (-6, 13) • B’ (-6, 1) • B’ (-2, 13) • B’ (-2, 1)

26. #25 • If a figure is in Quadrant I, and is rotated 270° clockwise, in which quadrant will the rotated image appear? • Quadrant I • Quadrant II • Quadrant III • Quadrant IV

27. #26 • Point P has coordinates (-7, 1). Point P’ is the image of P after a reflection across the y-axis. What are the coordinates of P’? • (7, -1) • (-1, 7) • (7, 1) • (1, 7)

28. #27 • Point Q has coordinates (-2, -5). Point Q’ is the image of Q after a reflection across the x-axis. What are the coordinates of Q’? • (5, -2) • (-5, -2) • (2, 5) • (-2, 5)

29. #28 • Point K’ (-3, 6) is the image of point K (3, 6) after a transformation. Which of the following could be that transformation? • A translation of 3 units to the left and 6 units up. • A reflection across the y-axis • A reflection across the x-axis • A rotation of 180°