Question

M (6, -2) is rotated 270° counterclockwise. What are the coordinates of M'?

Answer 1

To perform a 270° counterclockwise rotation of the point \( M(6, -2) \), we can use the rotation formula. The general rule for rotating a point \( (x, y) \) counterclockwise around the origin by an angle \( \theta \) degrees is:

\[
(x', y') = (x \cos \theta - y \sin \theta, x \sin \theta + y \cos \theta)
\]

For a 270° rotation, we can use the trigonometric values:

\[
\cos(270°) = 0
\]
\[
\sin(270°) = -1
\]

Now, applying this to the point \( (6, -2) \):

\[
x' = 6 \cdot 0 - (-2) \cdot (-1) = 0 - 2 = -2
\]
\[
y' = 6 \cdot (-1) + (-2) \cdot 0 = -6 + 0 = -6
\]

Thus, the coordinates of \( M' \) after a 270° counterclockwise rotation are:

\[
M'(-2, -6)
\]

So, the final answer is:

\[
\boxed{(-2, -6)}
\]