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Symmetry — Unit test Answers

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On a coordinate plane, 3 triangles are shown. Triangle A B C has points (5, negative 5), (1, negative 2), (1, negative 5). Triangle A prime B prime C prime has points (5, 5), (1, 2), (1, 5). Triangle A double-prime B double-prime C double prime has points (negative 1, 3), (negative 5, 0), (negative 5, 3).

Question illustration
A
Translation of negative 6 units x, negative 2 units y composition reflection across the x-axis
Option A
B
Reflection across the x-axis composition translation of negative 6 units x, negative 2 units y
Option B
C
Translation of negative 6 units x, negative 2 units y composition 90 degree rotation about point 0
Option C
D
90 degree rotation about point 0 translation of negative 6 units x, negative 2 units y
Option D
2
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Square PQRS is transformed as shown on the graph.

Question illustration
A
R0, 90°
B
R0, 180°
C
R0, 270°
D
R0, 360°
3

Triangle ABC was transformed to create triangle DEF.

Question illustration
A
corresponds to because they are about the same length.
Option A
B
corresponds to because they are in the same position.
Option B
C
corresponds to because the transformation is isometric.
Option C
D
corresponds to because the length is not preserved.
Option D
4

A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes the translation?

A
T1, –9(x, y)
B
T–1, –9(x, y)
C
T–9, 1(x, y)
D
T–9, –1(x, y)
5

A point has the coordinates (m, 0) and m ≠ 0.Which reflection of the point will produce an image located at (0, –m)?

A
a reflection of the point across the x-axis
B
a reflection of the point across the y-axis
C
a reflection of the point across the line y = x
D
a reflection of the point across the line y = –x
6

A transformation of ΔDEF results in ΔD'E'F'.

Question illustration
A
The transformation is a dilation.
B
The transformation is a reflection.
C
The transformation is a rotation.
D
The transformation is a translation.
7

A composition of transformations maps ΔKLM to ΔK"L"M".

Question illustration
A
a 90° rotation about point L
B
a 270° rotation about point L
C
a 90° rotation about point P
D
a 270° rotation about point P
8

On a coordinate plane, 2 quadrilaterals are shown. The first figure has points A (negative 2, 1), B (negative 4, 1), C (negative 4, 5), and D (negative 2, 4). Figure 2 has points A prime (2, 1), B prime (4, 1), C prime (4, 5), and D prime (2, 4).

Question illustration
A
rx-axis(x, y) → (–x, y)
B
ry-axis(x, y) → (–x, y)
C
rx-axis(x, y) → (x, –y)
D
ry-axis(x, y) → (x, –y)
9

Which rules could describe the rotation? Select two options.

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
(x, y) → (–y, x)
E
(x, y) → (y, –x)
10

On a coordinate plane, 2 triangles are shown. The first triangle has points F (3, 2), H (4, 5), G (1, 2). The second triangle has points F prime (negative 2, 3), H prime (negative 5, 4), G prime (negative 2, 1).

Question illustration
A
Correct. He transformed the triangle according to the rule (x, y) → (–y, x).
B
Incorrect. He transformed the triangle according to the rule (x, y) → (y, –x)
C
Incorrect. He transformed the triangle according to the rule (x, y) → (–y, –x)
D
Incorrect. He transformed the triangle according to the rule (x, y) → (–x, –y)
11

Which statement describes the order of rotational symmetry for an isosceles triangle?

A
An isosceles triangle has an order 0 rotational symmetry because there is no angle at which it can be rotated onto itself.
B
An isosceles triangle has an order 1 rotational symmetry because it does not have all congruent angles.
C
An isosceles triangle has an order 2 rotational symmetry because it has 1 pair of congruent angles.
D
An isosceles triangle has an order 3 rotational symmetry because it has 3 angles.
12

On a coordinate plane, 5 trapezoids are shown. Trapezoid L M N P is in quadrant 2 and has points (negative 2, 3), (negative 2, 6), (negative 1, 6), and (negative 1, 4). Trapezoid B is reflected in quadrant 2. Trapezoid C is reflected across the y-axis. Trapezoid D is reflected into quadrant 4. Trapezoid A is reflected across the x-axis.

Question illustration
A
figure A
B
figure B
C
figure C
D
figure D
13

What mistakes did he make? Select two options.

A
He applied the reflection to the pre-image first.
B
He applied the rotation to the pre-image first.
C
He changed the size of the figure instead of just applying a rotation.
D
He used point P as the center of rotation.
E
He used an incorrect angle of rotation around point P.
14

Which statements are true about trapezoid ABCD and its translated image, A'B'C'D'? Select two options.

A
The rule for the translation can be written as T–3, 1(x, y).
B
The rule for the translation can be written as T–1, 3(x, y).
C
The rule for the translation can be written as(x, y) → (x + 1, y – 3).
D
The rule for the translation can be written as(x, y) → (x – 3, y + 1).
E
Trapezoid ABCD has been translated 3 units to the right and 1 unit up.
15

A regular decagon has 10 sides.

Question illustration
A
5
B
10
C
15
D
20

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