AnswersAZ-Common Core Geometry AIntroduction to Transformations

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The rule as a mapping for the translation of a rectangle is (x, y) → (x – 2, y + 7). Which describes this translation?

A
a translation of 2 units down and 7 units to the right
B
a translation of 2 units down and 7 units to the left
C
a translation of 2 units to the right and 7 units up
D
a translation of 2 units to the left and 7 units up
2
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Rectangle EFGH is translated according to the rule T–5, 9(x, y). If the coordinates of the pre-image of point H are (–2, –3), what are the coordinates of H'?

A
(7, –8)
B
(–7, 6)
C
(3, –12)
D
(2, 1)
3

Hexagon DEFGHI is translated 8 units down and 3 units to the right. If the coordinates of the pre-image of point F are(–9, 2), what are the coordinates of F'?

A
(–17, 5)
B
(–6, –6)
C
(–17, –1)
D
(–12, –6)
4

On a coordinate plane, a triangle has points A prime (1, 2), B prime (3, negative 3), C prime (negative 1, negative 3).

Question illustration
A
(3.5, –9.2)
B
(–2.7, –4.7)
C
(–5.5, 3.2)
D
(0.7, –1.3)
5

A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?

A
(x, y) → (x + 5, y – 3)
B
(x, y) → (x + 5, y + 3)
C
(x, y) → (x – 3, y + 5)
D
(x, y) → (x + 3, y + 5)
6

Square ABCD was translated using the rule (x, y) → (x – 4, y + 15) to form A'B'C'D'. What are the coordinates of point D in the pre-image if the coordinates of point D’ in the image are (9, –8)?

A
(13, –23)
B
(5, 7)
C
(18, 1)
D
(–6, –4)
7

Triangle ABC was translated according to the rule (x, y) → (x + 1.5, y – 3.5) to create the image ΔA'B'C' shown on the coordinate plane.Which graph shows the pre-image, ΔABC?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

On a coordinate plane, a parallelogram has points A (negative 3, 4), B (3, 4), C (1, negative 2), and D (negative 5, negative 2).

Question illustration
A
(–5, –2)
B
(1, –12)
C
(4, –15)
D
(–9, –6)
9

A triangle on a coordinate plane is translated according to the rule T–3, 5(x, y). Which is another way to write this rule?

A
(x, y) → (x – 3, y + 5)
B
(x, y) → (x – 3, y – 5)
C
(x, y) → (x + 3, y – 5)
D
(x, y) → (x + 3, y + 5)
10

On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, negative 1), B (4, negative 1), C (4, negative 3), D (negative 2, negative 3). The second rectangle has points A prime (negative 5, 1), B prime (1, 1), C prime (1, negative 1), D prime (negative 5, negative 1).

Question illustration
T
T–3, 2(x, y)
T
T2, –3(x, y)
T
T3, 2(x, y)
T
T–2, 3(x, y)
11

On a coordinate plane, a triangle has points A (negative 2, negative 2), B (1, negative 5), and C (negative 5, negative 5).

Question illustration
A
(1, –5)
B
(–4, –10)
C
(–3, –12)
D
(3, –12)
12

A triangle on a coordinate plane is translated according to the rule T–8, 4(x, y). Which is another way to write this rule?

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)
13

On a coordinate plane, 2 parallelograms are shown. The first parallelogram has points A (negative 4, 4), B (negative 2, 4), C (negative 5, 1), D (negative 2, 1). The second parallelogram has points A prime (negative 2, 5), B prime (1, 5), C prime (negative 3, 2), D prime (0, 2).

Question illustration
A
T1, –2(x, y)
B
T1, 2(x, y)
C
T–2, 1(x, y)
D
T2, 1(x, y)
14

For the transformation to be a translation, which statements must be true? Select four options.

A
LL'=PP'
B
LL'=MM'
C
Trapezoid LMNP is congruent to trapezoid L'M'N'P'.
D
NN'=PP'
Option D
E
All line segments that connect a point on the pre-image to its corresponding point on the image are parallel.
15

Rectangle ABCD has vertices A(–6, –2), B(–3, –2),C(–3. –6), and D(–6, –6). The rectangle is translated so that the coordinates of the image are A’(–10, 1), B’(–7,1),C’(–7, –3), and D’(–10, –3).

A
T–4, 3(x, y)
B
T–4, 1(x, y)
C
T4, –1(x, y)
D
T4, –3(x, y)
16

Which statements are true about triangle ABC and its translated image, A'B'C'? Select two options.

A
The rule for the translation can be written as T–5, 3(x, y).
B
The rule for the translation can be written as T3, –5(x, y).
C
The rule for the translation can be written as(x, y) → (x + 3, y – 3).
D
The rule for the translation can be written as(x, y) → (x – 3, y – 3).
E
Triangle ABC has been translated 3 units to the right and 5 units down.

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