Question

Rectangle STUV with vertices S at (-7, 6), T at (-2, 6), U at (-2, 1), and V at (-7, 1). If rectangle STUV is translated using the rule (x, y) → (x − 2, y − 4) and then rotated 90° counterclockwise, what is the location of V″?

A) (3, -9)
B) (3, -4)
C) (-2, -4)
D) (-2, -9)

Answer 1

To find the location of V″, translate the rectangle using the given rule, and then rotate it 90° counterclockwise.

Step-by-step explanation:

To find the location of V″, we first need to translate the rectangle using the given rule (x, y) → (x − 2, y − 4). This means we subtract 2 from the x-coordinate and 4 from the y-coordinate of each vertex. After translation, the new vertices are S' at (-9, 2), T' at (-4, 2), U' at (-4, -3), and V' at (-9, -3).

Next, we need to rotate the translated rectangle 90° counterclockwise. This can be done by swapping the x and y coordinates and changing the sign of the new y-coordinate. The new vertices after rotation are S'' at (2, -9), T'' at (2, -4), U'' at (-3, -4), and V'' at (-3, -9).

Therefore, the location of V″ is ( -3, -9).