Question

Given a point on a line segment-4, 5) what is the new point when the point is rotated counterclockwise about the origin 270 degrees

Answer 1

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

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

In this case, the point is (-4, 5) and the rotation angle is 270 degrees counterclockwise.

Converting 270 degrees to radians:
270 degrees = (270 * π) / 180 = 3π / 2 radians.

Using the formula, we can substitute the values:

x' = (-4) * cos(3π / 2) - 5 * sin(3π / 2)
y' = (-4) * sin(3π / 2) + 5 * cos(3π / 2)

Calculating cosine and sine of 3π / 2:
cos(3π / 2) = 0
sin(3π / 2) = -1

Substituting the values:
x' = (-4) * 0 - 5 * (-1) = 0 + 5 = 5
y' = (-4) * (-1) + 5 * 0 = 4 + 0 = 4

Therefore, the new point after rotating (-4, 5) counterclockwise about the origin by 270 degrees is (5, 4).