Rotate the point (9, 5) on a geometric figure 270 degrees clockwise. What is the new point?

Answer 1

To rotate a point clockwise by 270 degrees, we can use the following transformation:

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

Where (x', y') is the new point, (x, y) is the original point, and θ is the angle of rotation.

Given the original point (9, 5) and the angle of rotation 270 degrees, we can substitute these values into the formula:

(x', y') = (9cos(270°) - 5sin(270°), 9sin(270°) + 5cos(270°))

Now, let's calculate:

sin(270°) = -1
cos(270°) = 0

(x', y') = (9cos(270°) - 5sin(270°), 9sin(270°) + 5cos(270°))
= (9(0) - 5(-1), 9(-1) + 5(0))
= (0 - (-5), -9 + 0)
= (0 + 5, -9)
= (5, -9)

Therefore, the new point after rotating (9, 5) by 270 degrees clockwise is (5, -9).