Question

Identify the point that applies a rotation function mapping for P in a 270-degree counterclockwise rotation about the origin.

A 270-degree counterclockwise rotation about the origin will plot P' at point __.

Point P: (4, 1)
Point 1: (-1, 4)
Point 2: (-4, -1)
Point 3: (-1, -4)
Point 4: (1, -4)

Answer 1

To apply a 270-degree counterclockwise rotation about the origin, we can use the rotation transformation formulas. The formula for rotating a point \( (x, y) \) by 270 degrees counterclockwise is given by:

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

For point \( P \) which is at \( (4, 1) \):

\[
x = 4, \quad y = 1
\]

Applying the rotation:

\[
x' = y = 1
\]
\[
y' = -x = -4
\]

Thus, the new coordinates after the rotation \( P' \) will be:

\[
P' = (1, -4)
\]

Therefore, the point \( P' \) will be at point **(1, -4)**.

The correct answer is **Point 4: (1, -4)**.