What is the new point when you rotate a geometric figure with point (5, 8) 270 degrees counterclockwise about the origin?
To rotate a point counterclockwise about the origin, you can use the following formula:
(x', y') = (x * cosθ - y * sinθ, x * sinθ + y * cosθ)
Where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the new point, and θ is the angle of rotation.
In this case, the original point is (5, 8) and the angle of rotation is 270 degrees counterclockwise.
Using the formula:
(x', y') = (5 * cos(270°) - 8 * sin(270°), 5 * sin(270°) + 8 * cos(270°))
Now, let's evaluate the trigonometric functions:
cos(270°) = 0
sin(270°) = -1
(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 degrees counterclockwise about the origin is (8, -5).