Question

P (1, - 4) is rotated 270° clockwise.

What are the coordinates of P'?

Answer 1

To rotate the point \( P (1, -4) \) by \( 270^\circ \) clockwise, we can first convert this rotation into a more manageable form. A \( 270^\circ \) clockwise rotation is equivalent to a \( 90^\circ \) counterclockwise rotation.

The general formula for rotating a point \( (x, y) \) by \( 90^\circ \) counterclockwise is:

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

Let's apply this formula step-by-step:

1. Identify the coordinates of point \( P \):
- \( x = 1 \)
- \( y = -4 \)

2. Apply the rotation formula:
\[
P' = (-y, x) = (-(-4), 1) = (4, 1)
\]

So, the coordinates of point \( P' \) after a \( 270^\circ \) clockwise rotation of point \( P (1, -4) \) are:

\[
\boxed{(4, 1)}
\]