Question

1. in the coordinate - plane, a rectangle with vertices at (0,0), (3,0), (3,2), (0,2) is transformed using a reflection across the y - axis followed by a translation 4 units up. what are the coordinates of the transformed rectangles vertices?

a. (3,4), (0,4), (0,6), (3,6)
b. (0,4), (3,4), (3,6), (0,6)
c. (0,0), (- 3,0), (- 3,2), (0,2)
d. (0,4), (- 3,4), (- 3,6), (0,6)

1. given these two similar figures, describe the transformation from the pre - image (figure a) to the image (figure b).

a. the figure has been rotated and translated.
b. the figure has been translated and dilated.
c. the figure has been dilated and rotated.
d. the figure has been translated and rotated.

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the y - axis, the transformation is $(-x,y)$. The original rectangle has vertices $(0,0),(3,0),(3,2),(0,2)$. After reflection across the y - axis, the vertices become $(0,0),(- 3,0),(-3,2),(0,2)$.

Step2: Recall translation rule

A translation of 4 units up means adding 4 to the y - coordinate of each point. So, $(0,0)$ becomes $(0,4)$, $(-3,0)$ becomes $(-3,4)$, $(-3,2)$ becomes $(-3,6)$ and $(0,2)$ becomes $(0,6)$.

Answer:

d. $(0,4),(-3,4),(-3,6),(0,6)$