Question

What would be the new coordinates after rotating (3,6) 270 degree counterclockwise?

Answer 1

To rotate the point (3, 6) by 270 degrees counterclockwise around the origin, we can use the rotation formula for a point \((x, y)\):

\[
(x', y') = (y, -x)
\]

For a 270-degree counterclockwise rotation, the transformation can also be thought of as equivalent to a 90-degree clockwise rotation.

1. Start with the original coordinates: \((3, 6)\).
2. Apply the transformation:

\[
x' = y = 6
\]
\[
y' = -x = -3
\]

Thus, the new coordinates after rotating (3, 6) by 270 degrees counterclockwise are \((6, -3)\).