Translations and Reflections Practice

Question

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Question
Use the image to answer the question.

A trapezoid with vertices upper A prime, upper B prime, upper C prime, and upper D prime is shaded inside and plotted on a coordinate plane. The x and y axes range from negative 5 to 5 in increments of 1. The coordinates of trapezoid upper A prime B prime C prime D prime are as follows: vertex upper A prime at left parenthesis negative 2 comma negative 1 right parenthesis, vertex upper B prime at left parenthesis negative 4 comma negative 3 right parenthesis, vertex upper C prime at left parenthesis 2 comma negative 3 right parenthesis, and vertex upper D prime at left parenthesis 2 comma negative 1 right parenthesis.

Trapezoid A′B′C′D′ is a translation of a preimage trapezoid that was shifted 4 units to the right and 5 units down. What are the coordinates of A , B , C , and D of the preimage trapezoid?

(2 points)

Answer 1

To find the coordinates of the preimage trapezoid, we need to reverse the translation that was applied to the image trapezoid.

1. For the x-coordinates:
- A's x-coordinate was shifted 4 units to the right to become -2, so we need to subtract 4 from -2 to get the original x-coordinate of A: -2 - 4 = -6
- B's x-coordinate was shifted 4 units to the right to become -4, so we need to subtract 4 from -4 to get the original x-coordinate of B: -4 - 4 = -8
- C's x-coordinate was shifted 4 units to the right to become 2, so we need to subtract 4 from 2 to get the original x-coordinate of C: 2 - 4 = -2
- D's x-coordinate was shifted 4 units to the right to become 2, so we need to subtract 4 from 2 to get the original x-coordinate of D: 2 - 4 = -2

2. For the y-coordinates:
- A's y-coordinate was shifted 5 units down to become -1, so we need to subtract 5 from -1 to get the original y-coordinate of A: -1 - 5 = -6
- B's y-coordinate was shifted 5 units down to become -3, so we need to subtract 5 from -3 to get the original y-coordinate of B: -3 - 5 = -8
- C's y-coordinate was shifted 5 units down to become -3, so we need to subtract 5 from -3 to get the original y-coordinate of C: -3 - 5 = -8
- D's y-coordinate was shifted 5 units down to become -1, so we need to subtract 5 from -1 to get the original y-coordinate of D: -1 - 5 = -6

Therefore, the coordinates of the preimage trapezoid are:
- A: (-6, -6)
- B: (-8, -8)
- C: (-2, -8)
- D: (-2, -6)