What is the new point when you rotate a geometric figure with point (5,8) 270° counterclockwise about to the origin? (-8,-5), (-5,8), (8,5), (8,-5)

Answer 1

To rotate a point counterclockwise about the origin, you can use the following rotation formula:

(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)

where (x, y) is the original point, (x', y') is the rotated point, and θ is the angle of rotation counterclockwise.

In this case, the original point is (5, 8) and the angle of rotation is 270° counterclockwise. Therefore, θ = 270°.

Using the rotation formula, we can calculate:

(x', y') = (5cos270° - 8sin270°, 5sin270° + 8cos270°)

Since cos270° = 0 and sin270° = -1, the formula simplifies to:

(x', y') = (5(0) - 8(-1), 5(-1) + 8(0))

(x', y') = (0 + 8, -5 + 0)

(x', y') = (8, -5)

Therefore, the new point after rotating (5, 8) 270° counterclockwise about the origin is (8, -5).