What is the new point when you rotate a geometric figure with point (5, 8) 270 degrees counterclockwise about the origin?(1 point)
Responses
(8, −5)
(−8, −5)
(8, 5)
(−5, 8)
To rotate a point (x, y) 270 degrees counterclockwise about the origin, we switch the coordinates and negate the new x-coordinate.
In this case, the original point is (5, 8). When we rotate it 270 degrees counterclockwise, the new point will be (-8, 5).
Thus, the correct answer is (−8, 5).
To rotate a point counterclockwise about the origin, you can use the following formula:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
In this case, the point is (5, 8) and the angle of rotation is 270 degrees.
Plugging in the values:
x' = 5 * cos(270) - 8 * sin(270)
y' = 5 * sin(270) + 8 * cos(270)
cos(270) = 0
sin(270) = -1
x' = 5 * 0 - 8 * -1 = 0 + 8 = 8
y' = 5 * -1 + 8 * 0 = -5 + 0 = -5
Therefore, the new point after rotating (5, 8) 270 degrees counterclockwise about the origin is (8, -5).
The correct answer is:
(8, −5)