Question
Rectangle PQRS is rotated 90° counterclockwise about the origin.
On a coordinate plane, rectangle P Q R S has points (2, 3), (5, 3), (5, 1), (2, 1).
What are the coordinates of point Q’?
Q’( –3, 5)
Q’(3, –5)
Q’(5, –3)
Q’(–5, –3)
On a coordinate plane, rectangle P Q R S has points (2, 3), (5, 3), (5, 1), (2, 1).
What are the coordinates of point Q’?
Q’( –3, 5)
Q’(3, –5)
Q’(5, –3)
Q’(–5, –3)
Answers
GPT-4o mini
To rotate a point \((x, y)\) 90° counterclockwise about the origin, you can use the transformation:
\[
(x', y') = (-y, x)
\]
For point \(Q(5, 3)\):
1. Substitute \(x = 5\) and \(y = 3\) into the transformation:
\[
x' = -y = -3
\]
\[
y' = x = 5
\]
So the new coordinates for point \(Q'\) after the rotation are \((-3, 5)\).
Thus, the coordinates of point \(Q'\) are:
**Q’( –3, 5)**.
\[
(x', y') = (-y, x)
\]
For point \(Q(5, 3)\):
1. Substitute \(x = 5\) and \(y = 3\) into the transformation:
\[
x' = -y = -3
\]
\[
y' = x = 5
\]
So the new coordinates for point \(Q'\) after the rotation are \((-3, 5)\).
Thus, the coordinates of point \(Q'\) are:
**Q’( –3, 5)**.