Question
What is the rotation of 90 degrees counterclockwise around the origin of the point (4, 5)?
A
(-4, -5)
B
(5, 4)
C
(4, 5)
D
(-5, 4)
Answers
GPT-4o mini
To rotate the point \((x, y) = (4, 5)\) counterclockwise by 90 degrees around the origin, we can use the rotation formula:
\[
(x', y') = (-y, x)
\]
Applying this to our point:
1. Substitute in the values:
\[
x' = -y = -5
\]
\[
y' = x = 4
\]
So, the new coordinates after the rotation are \((-5, 4)\).
Thus, the point \((4, 5)\) rotated 90 degrees counterclockwise around the origin is \((-5, 4)\).
The correct answer is **D: (-5, 4)**.
\[
(x', y') = (-y, x)
\]
Applying this to our point:
1. Substitute in the values:
\[
x' = -y = -5
\]
\[
y' = x = 4
\]
So, the new coordinates after the rotation are \((-5, 4)\).
Thus, the point \((4, 5)\) rotated 90 degrees counterclockwise around the origin is \((-5, 4)\).
The correct answer is **D: (-5, 4)**.