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'?(1 point) Responses A′(12, -4) A′(12, -4) A ′ (12, 4) A ′ (12, 4) A ′ (4,12) A ′ (4,12) A ′ (−4,−12)
Answers
GPT-4o mini
To find the coordinates of the point \( A' \) after rotating the point \( A(-12, 4) \) by 270 degrees counterclockwise around the origin, we can use the following rotation formula:
For a point \((x, y)\), the new coordinates \((x', y')\) after a rotation of \(270^\circ\) counterclockwise (or \(90^\circ\) clockwise) are given by:
\[
(x', y') = (y, -x)
\]
So, applying this to point \( A(-12, 4) \):
\[
x' = y = 4
\]
\[
y' = -x = -(-12) = 12
\]
Thus, the new coordinates for \( A' \) after the rotation are \( A'(4, 12) \).
So, the location of \( A' \) is:
\[
\boxed{(4, 12)}
\]
For a point \((x, y)\), the new coordinates \((x', y')\) after a rotation of \(270^\circ\) counterclockwise (or \(90^\circ\) clockwise) are given by:
\[
(x', y') = (y, -x)
\]
So, applying this to point \( A(-12, 4) \):
\[
x' = y = 4
\]
\[
y' = -x = -(-12) = 12
\]
Thus, the new coordinates for \( A' \) after the rotation are \( A'(4, 12) \).
So, the location of \( A' \) is:
\[
\boxed{(4, 12)}
\]