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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?
7
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)