Download REVIEW: Transformations and Congruence

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REVIEW: Transformations and Congruence
Use trapezoid GHIJ.
5. The ordered pair R( 2, 7) is translated 5 units to the
right and down 2 units. Use an algebraic representation
to describe the translation.
6. Triangle FGH has vertices F(3, 1), G(5, 1), and
H(5, 2). What are the coordinates of the image of point
H after a translation 1 unit to the right and 3 units down?
1. If the figure is translated 3 units left and 4 units down,
what are the coordinates of G' ?
7. Quadrilateral JKLM has vertices J ( 4, 4), K( 4, 1),
L(1, 1), and M(1, 4). What are the coordinates of the
image of point K after a reflection across the x-axis?
2. If the figure is rotated 90 clockwise about the origin,
what are the coordinates of H' ?
3. If the figure is reflected over the y-axis, what are the
coordinates of I' ?
8. Write congruence statements comparing the
corresponding parts in the congruent quadrilaterals
ABCD and EFGH.
4. After a translation, the coordinates of J' are ( 3, 4).
Represent the translation algebraically.
a. (x, y)
(x 3, y 4)
b. (x, y)
(x 2, y 5)
c. (x, y)
(x 2, y 4)
d. (x, y)
(x 3, y 5)
Angle Statements:
Side Statements:
9. Determine if the two figures shown at the right are
congruent by using transformations. Explain your
reasoning.
12. Graph and label the image of
reflection over the y-axis.
YZW after a
Transformations:
13. What will be the coordinates of triangle Y' Z' W' if
trianlge YZW is reflected across the y-axis and translated
3 units down?
Refer to the graph of
YZW below.
a. Y” (4, 1), Z” ( 4, 1), W” (0, 7)
b. Y” (4, 1), Z” ( 4, 1), W” (0, 7)
c. Y” (4, 1), Z” ( 4, 1), W” (0, 7)
d. Y” (4, 1), Z” ( 4, 1), W” (0, 7)
14. Triangle ABC has vertices A(3, 2), B( 2, 3), and
C(1, 3). The triangle is reflected over the x-axis and
then translated 2 units left to form triangle A'B'C' . What
are the coordinates of A', B' , and C' ?
10. Graph and label the image of YZW after a
translation 2 units right and 1 unit down.
11. YZW is translated 2 units right and 1 unit down.
Write an algebraic expression to describe the translation.
a. (x, y)
(x 2, y 1)
b. (x, y)
(x 2, y + 1)
c. (x, y)
(x 2, y + 1)
d. (x, y)
(x 1, y + 2)
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15. Quadrilateral KLMN has vertices K(2, 1), L(5, 2),
M(7, 5), N(4, 4). The quadrilateral is rotated 90
clockwise about the origin and then translated 1 unit
down. What are the coordinates of the vertices of
quadrilateral K'L'M'N' ?
18. If point A is translated 5 units left and 2 units down,
what will be the coordinates of point A in its new
position?
Rotation Steps:
Translation Steps:
16. Triangle ABC has vertices
,
and
. Graph the vertices of triangle
a translation of 5 units right and 6 units up.
after
17. Triangle ABC with vertices A(–3, 2), B(–8, 8), and
C(–3, –2) translated 2 units up and 8 units right
19. Construct the reflection over the x-axis of the
trapezoid given below:
20. Find the coordinates of the vertices of the figure
after a reflection over the x-axis. Then graph the
reflection image.
20. x-axis
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21. A rectangle with vertices A(4, –4), B(4, –8), C(6, –
8)and D(6, –4) is rotated 270° clockwise about the
origin.
25. Determine if the two figures are congruent by using
transformations.
22. A triangle with vertices L(–3, 5), M(–3, 9), and N(–9,
5) is rotated 180° counterclockwise about the origin.
23. Identify the coordinates for the triangle ABC, when it
is rotated clockwise about the origin by
.
a. The figures are congruent because a
reflection followed by a rotation will map
figure M onto figure N.
b. The figures are congruent because a
translation followed by a rotation will map
figure M onto figure N.
c. The figures are congruent because a rotation
followed by a translation will map figure M
onto figure N.
d. The figures are not congruent. No
transformations will match the two figures
up exactly.
26. In the figure below,
NO = 24, and MO = 26, what is LP?
. If MN = 10,
24. Triangle XYZ has vertices at (1, 1), (1, 5), and (3, 5).
27. Write congruence statements comparing the
corresponding parts in the congruent figures below.
a. Translate XYZ 3 units down, then reflect it over the
y-axis. Label the vertices of the image X'Y'Z'.
b. Find the lengths of the sides of XYZ and X'Y'Z'.
c. Are the triangles congruent? Justify your answer.
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Answer Key
1. b
28. When reflected across the y-axis, the x-coordinate
becomes its opposite.
2. c
3. a
4. b
5. d
6. c
7. b
8. a
9. a
(–2, 3), (–4, 1), (–4, –4), (–2, –2)
10. c
29.
11. a
12. b
,
,
,
,
,
,
,
30. a. X' (–1, –2), Y' (–1, 2), Z' (–3, 2)
13. c
14. d
15. c
16. b
17. c
18. b
19. d
20. b
21. d
22. c
b. XYZ: XY = 4 units, YZ = 2 units, and XZ =
units
X'Y'Z': X'Y' = 4 units, Y'Z' = 2 units, and X'Z' =
units
c. Yes; Sample answer: The matching sides are the same
length.
23. a
24. b
25. a
26. d
27. c
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