Question

Rectangle stuv is shown on a coordinate plane. 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 v³?

1) (3, -9)
2) (3, -4)
3) (-2, -4)
4) (-2, -9)

Answer 1

The location of v³ after the given transformations is (3, -9).

Step-by-step explanation:

To find the location of v³, we need to follow the given transformations. First, we translate the rectangle by subtracting 2 from the x-coordinate and 4 from the y-coordinate. So, the new coordinates for v are (-7 - 2, 1 - 4) which is (-9, -3). Next, we rotate the translated rectangle 90° counterclockwise. This means that the x-coordinate becomes the negative of the y-coordinate and the y-coordinate becomes the positive of the x-coordinate. So, the final location of v³ is (-(-3), -9) which simplifies to (3, -9).