AnswersPARTA - EOP PGCPS GEOMETRY OC FALL2026 - 793413Slopes of Parallel and Perpendicular Lines

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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)
2
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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
(
(1, –5)
(
(–4, –10)
(
(–3, –12)
(
(3, –12)
3

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)
4

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)
5

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
6

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)
7

Triangle ABC is translated according to the rule (x, y) → (x + 2, y – 8). If the coordinates of the pre-image of point B are(4, –5), what are the coordinates of B'?

(
(2, 3)
(
(1, –9)
(
(–3, –4)
(
(6, –13)
8

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)
9

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)
10

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)
11

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
12

Triangle ABC is translated according to the rule (x, y) → (x + 2, y – 8). If the coordinates of the pre-image of point B are(4, –5), what are the coordinates of B'?

A
(2, 3)
B
(1, –9)
C
(–3, –4)
D
(6, –13)
13

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)
14

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.
15

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
T
T1, –2(x, y)
T
T1, 2(x, y)
T
T–2, 1(x, y)
T
T2, 1(x, y)
16

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
On a coordinate plane, a triangle has points A (0.5, negative 1.5), B (0.5, negative 4.5), C (negative 3.5, negative 4.5).
Option A
B
On a coordinate plane, a triangle has points A (2.5, 0.5), B (2.5, 2.5), C (negative 1.5, negative 2.5).
Option B
C
On a coordinate plane, a triangle has points A (negative 4.5, 3.5), B (negative 4.5, 0.5), C (negative 8.5, 0.5).
Option C
D
On a coordinate plane, a triangle has points A (negative 2.5, 5.5), B (negative 2.5, 2.5), C (negative 6.5, 2.5).
Option D
17

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)
18

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)
19

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.
20

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.

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