Question

What is a new point when you rotate a geometric figure with point (5, 8) 270 degrees counterclockwise about the origin.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

When a geometric figure is rotated 270 degrees counterclockwise about the origin, each point of the figure is moved to a new location. The formula to find the new coordinates after a counterclockwise rotation is:

x' = x * cos(angle) - y * sin(angle)
y' = x * sin(angle) + y * cos(angle)

In this case, the given point is (5, 8), and the rotation angle is 270 degrees counterclockwise. Plugging these values into the formula:

x' = 5 * cos(270) - 8 * sin(270)
y' = 5 * sin(270) + 8 * cos(270)

The cosine of 270 degrees is 0, and the sine of 270 degrees is -1. Plugging these values into the formula:

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

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