Question

Please help!! Polygon ABCDE is the first in a pattern for a high school project. The polygon is transformed so that the image of A’ is at (-2,4) and the image of D’ is at (-1,2). Which transformation can be used to show that ABCDE and its image are congruent?

A. Rotate ABCDE 90 degrees counterclockwise
B. Translate ABCDE left 4 units and down 2 units
C. Reflect ABCDE over the y-axis
D. Rotate ABCDE 90 degrees clockwise

Answer 1

The transformation that can be used to show that polygon ABCDE and its image are congruent is B. Translate ABCDE left 4 units and down 2 units.

Step-by-step explanation:

To understand why, let's consider the given coordinates of the image points.

The image point A' is at (-2,4) and the image point D' is at (-1,2).

To obtain the image, we have to move A and D by the same amount in the same direction.

In this case, we need to move A 4 units left and 2 units down, and we need to move D 4 units left and 2 units down as well.

This corresponds to a translation of ABCDE left 4 units and down 2 units.

By translating, we are preserving the shape and size of the polygon, which means ABCDE and its image are congruent.

So therefore the correct answer is B. Translate ABCDE left 4 units and down 2 units.