Question

A quadrilateral with vertices A(-12, 4), B -8, -4), C(0, 4), and D(2, 0) is rotated 270 degrees counter clockwise. What is the location of A'?

Answer 1

To rotate a point \( (x, y) \) 270 degrees counterclockwise around the origin, we can use the following transformation formula:

\[
(x, y) \to (y, -x)
\]

Using this formula, let's transform the coordinates of point \( A(-12, 4) \):

1. Identify the coordinates of point \( A \):
- \( x = -12 \)
- \( y = 4 \)

2. Apply the rotation transformation:
- The new \( x \) coordinate will be \( y = 4 \).
- The new \( y \) coordinate will be \( -x = -(-12) = 12 \).

So after the rotation, the new coordinates of point \( A' \) are:

\[
A' = (4, 12)
\]

Thus, the location of \( A' \) after a 270-degree counterclockwise rotation is \( \boxed{(4, 12)} \).