Question

The image of a point on a coordinate plane is at P'(-2,7). Find the preimage before a 270 degree ( counterclockwise)rotation about the origin.

Answer 1

To find the preimage of a point after a 270-degree counterclockwise rotation about the origin, we need to apply the inverse rotation to the given image point \( P'(-2, 7) \). A 270-degree counterclockwise rotation can be treated as a 90-degree clockwise rotation, as rotating 270 degrees counterclockwise is equivalent to rotating 90 degrees clockwise.

To rotate a point \( (x, y) \) 90 degrees clockwise, we use the following transformation:

\[
(x, y) \rightarrow (y, -x)
\]

Now, applying this transformation to the point \( P'(-2, 7) \):

- Here, \( x = -2 \) and \( y = 7 \).
- So, the preimage \( P(x, y) \) will be:

\[
P(-2, 7) \rightarrow (7, -(-2)) = (7, 2)
\]

Thus, the preimage of the point \( P'(-2, 7) \) before a 270-degree counterclockwise rotation about the origin is \( P(7, 2) \).