Identify the point that applies a rotation function mapping for P located at (4,1) in a 270-degree counterclockwise rotation about the origin.

Answer 1

To find the new coordinates of point P after a 270-degree counterclockwise rotation about the origin, we can use the rotation formula:

(x', y') = (x*cos(θ) - y*sin(θ), x*sin(θ) + y*cos(θ))

where (x', y') are the new coordinates after the rotation, (x, y) are the original coordinates, and θ is the angle of rotation.

In this case, the original coordinates are (4, 1) and the angle of rotation is 270 degrees.

Using the rotation formula, we can calculate the new coordinates:

(x', y') = (4*cos(270) - 1*sin(270), 4*sin(270) + 1*cos(270))

Since cos(270) = 0 and sin(270) = -1, we can simplify the equation:

(x', y') = (4*0 - 1*(-1), 4*(-1) + 1*0)

(x', y') = (0 + 1, -4 + 0)

(x', y') = (1, -4)

Therefore, the point P located at (4, 1) will move to the point (1, -4) after a 270-degree counterclockwise rotation about the origin.