Question

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″?

Answer 1

When rectangle STUV is translated using a given rule and then rotated 90° counterclockwise, the coordinates of V″ can be determined by applying the translation rule and the rotation to the original coordinates of V.

To find the location of V″ after the rectangle STUV is translated and then rotated, we need to follow these steps:

1. Apply the translation rule (x, y) → (x - 2, y - 4) to each vertex of the rectangle to get the new coordinates.
2. Rotate the translated rectangle 90° counterclockwise.
3. Identify the new coordinates of vertex V″.

Let's assume the original coordinates of V are (x, y). After the translation, the new coordinates will be (x - 2, y - 4). Now, we can apply a 90° counterclockwise rotation, where the x-coordinate becomes -y and the y-coordinate becomes x. Therefore, the new coordinates of V″ are (-y, x - 2).