Pre-Algebra- James Name: ___________________________

Congruent Transformations – Quiz Review Guide

1) a. Describe the translation that maps quadrilateral ABCD onto A’B’C’D’.

b. Name the properties that the translation preserved about ABCD.

c. Name a property that the translation changed about ABCD.

2) Draw the image of the figure after the translation: 3 units left and 9 units down. Label the vertices.

Use the graph for #3 – 5.

3) Quadrilateral J is reflected across the x-axis. What is the image of the reflection?

4) Which two quadrilaterals are reflections of each other across the y-axis?

5) How are quadrilaterals H and J related?

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6) a. Draw the image of the figure after a reflection across the x-axis.

b. Name a property that the reflection preserved about ABCD.

c. Name a property that the reflection changed about ABCD.

Use the figures at the right for #7 - 9. Figure A is to be rotated about the origin.

7) If you rotate figure A 90 counterclockwise, what quadrant will the image be in?

8) If you rotate figure A 180, what quadrant will the image be in?

9) Rotate figure A 90 clockwise. Label the image figure B.

10) Graph quadrilateral WXYZ with vertices W(2, -2), X(2, -5), Y(6, -5), and Z(3, -2). Then graph W’X’Y’Z’, the image of WZYX after a 90 counterclockwise rotation around the origin.

What property of WXYZ is perserved after the rotation?

Write an algebraic rule to describe each transformation of figure A to figure A′. Then describe the transformation.

11) 12)

13) Use the given rule to graph the image of each figure. Then describe the transformation.(x, y) (-x, y)

14) Triangle LMN has L at (1, -1) and M at (2, 3). Triangle L′M′N′ has L′ at (-1, -1) and M′ is at (3, -2). What type of transformation is this? Describe it.

15) What sequence of transformations is used to transform figure A to figure C? Express the transformations in words and algebraically.

16) Identify a sequence of transformations that will transform figure D into figure E.

17) A triangle with coordinates (6, 4) (2, -1), and (-3, 5) is translated 4 units left and rotated 180 about the origin. What are the coordinates of its image?

18) a. Graph triangle D’E’F’, the image of triangle DEF after a reflection across the y-axis.

b. On the same coordinate plane, graph triangle D’’ E’’ F’’, the image of triangle D’E’F’ after a translation of 7 units down and 2 units to the right.

c. Find a different sequence of transformations that will transform triangle DEF to triangle D’’E’’F’’.

Use triangle ABC for #19– 23.

19) ABC is translated 2 units right and 1 unit down. What is the new location of point C?

A (1, -7) C (2, -5) B (1, -3) D (4, -6)

20) Which property changes when a figure is translated?A side lengthsB angle measures C locationD orientation

21) Which translation moves a triangle 4 units to the right and 8 units up?A (x, y) (x - 4, y - 8)B (x, y) (x - 4, y + 8)C (x, y) (x + 8, y - 4)D (x, y) (x + 8, y + 4)

22) ABC is reflected across the x-axis. What is the new location of point B? A (-4, -2) C (4, -2) B (-4, 2) D (4, 2)

23) ∆ABC is rotated 90° counterclockwise with the origin as center of rotation. Where is the image of point A?

A (0, 0) C (2, -4)B (4, -2) D (2, 4)