Similar Figures Answers

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A has the coordinates (–4, 3) and B has the coordinates (4, 4). If DO,1/2(x, y) is a dilation of △ABC, what is true about the image △A'B'C'? Check all that apply.

A
AB is parallel to A'B'.
B
DO,1/2(x, y) =
Option B
C
The distance from A' to the origin is half the distance from A to the origin.
D
The vertices of the image are farther from the origin than those of the pre-image.
E
A'B' is greater than AB.
5

△RST is dilated with the rule DT,1/3 (x, y), where the center of dilation is T(3, –2).

Answers:
The distance between the x-coordinates of R and T is .:3
The distance between the y-coordinates of R and T is .:6
R' is from T, so the coordinates of R' are .:1 unit left, 2 units up
R' is from T, so the coordinates of R' are .:(2, 0)
6

Derek tried to dilate the isosceles trapezoid ABDC with the center of dilation at the origin with a scale factor of 2. Check his work and complete the statements.

Answers:
The slope of AC is .:4
The slope of EG is .:2
The polygons are not dilations of each other because .:the corresponding sides are not parallel
7

–201✔ 2

A
–2
B
0
C
1
D
✔ 2
8

the center of dilation is not at (0, 0)the coordinate G should be at (–1, 0)✔ the corresponding sides are not parallelAC and EG are corresponding sides

A
the center of dilation is not at (0, 0)
B
the coordinate G should be at (–1, 0)
C
✔ the corresponding sides are not parallel
D
AC and EG are corresponding sides
11

Which graph has figures that can undergo a similarity transformation to justify that they are similar?

A
[Image: On a coordinate plane, a small square and a rectan...]
Option A
B
[Image: On a coordinate plane, 2 rectangles are shown. The...]
Option B
C
[Image: On a coordinate plane, 2 rectangles are shown. The...]
Option C
D
[Image: On a coordinate plane, 2 rectangles are shown. The...]
Option D
12

Which composition of similarity transformations would map polygon ABDC to polygon A'B'D'C'?

A
a dilation with a scale factor greater than 1 and then a translation
B
a dilation with a scale factor greater than 1 and then a rotation
C
a dilation with a scale factor less than 1 and then a reflection
D
a dilation with a scale factor less than 1 and then a translation
13

△RST is dilated with the rule DT,1/3 (x, y), where the center of dilation is T(3, –2).

Answers:
The distance between the x-coordinates of R and T is .:3
The distance between the y-coordinates of R and T is .:6
R' is from T, so the coordinates of R' are .:1 unit left, 2 units up
R' is from T, so the coordinates of R' are .:(2, 0)
14

034✔ 6

A
0
B
3
C
4
D
✔ 6
15

1 unit left, 1 unit up✔ 1 unit left, 2 units up3 units left, 2 units up2 units left, 4 units up

A
1 unit left, 1 unit up
B
✔ 1 unit left, 2 units up
C
3 units left, 2 units up
D
2 units left, 4 units up
16

(0, 0)(0, 2)(1, 2)✔ (2, 0)

A
(0, 0)
B
(0, 2)
C
(1, 2)
D
✔ (2, 0)

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