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, we can use the following formulas:

new_x = old_x * cos(angle) - old_y * sin(angle)
new_y = old_x * sin(angle) + old_y * cos(angle)

In this case, the angle of rotation is 270 degrees. Converting this to radians, we have:

angle = 270 * (π/180) = 3π/2

Now, substituting the given point (-4, 5) into the formulas, we can calculate the new point:

new_x = (-4) * cos(3π/2) - 5 * sin(3π/2)
= 4 * 0 - (-5) * 1
= 5

new_y = (-4) * sin(3π/2) + 5 * cos(3π/2)
= (-4) * (-1) + 5 * 0
= 4

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