Rotation Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

Rotate the point

A(3, 2)

90°

counterclockwise about the origin. Where does A end up?

1
Step 1: The rule for 90° CCW rotation is $(x, y) \to (-y, x)$ .
2
Step 2: Apply to $A(3, 2)$ : $A' = (-2, 3)$ .
3
Step 3: Verify distance from origin is unchanged: $\sqrt{3^2+2^2} = \sqrt{13}$ and $\sqrt{(-2)^2+3^2} = \sqrt{13}$ . ✓

Answer

A' = (-2, 3)

The 90° CCW rotation rule

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

is derived from the rotation matrix with

\theta=90°

\cos90°=0

\sin90°=1

, giving

(-y, x)

. Rotation preserves distance from the center of rotation.

About Rotation

A rigid transformation that turns every point of a figure by a fixed angle around a fixed center of rotation.

Rotate the point [formula] by [formula] counterclockwise about the origin. Give exact coordinates.

What is the image of point [formula] after a [formula] rotation about the origin?

Triangle with vertices [formula], [formula], [formula] is rotated [formula] CCW about the point [for