Question

If P = (5,3), Find:
*270° (P)

Answer 1

To find the position of the point P = (5,3) after a 270° rotation around the origin, swap and then change the sign of the x-coordinate. The result is (-3, 5).

Step-by-step explanation:

To find the point P after a rotation of 270°, we can use the rotation matrix formula:

x' = x cos θ - y sin θ

y' = x sin θ + y cos θ

Let's plug in the coordinates for point P (5, 3) and rotate it 270°:

x' = 5 cos 270° - 3 sin 270°

y' = 5 sin 270° + 3 cos 270°

Using the trigonometric values, we get:

x' = 3

y' = -5

Therefore, after rotating point P 270°, the new coordinates are (3, -5).