Give an a point on a line segment negative four, five what is the new point when the point is rotated counterclockwise about the origin 270°

Answer 1

To rotate a point counterclockwise about the origin, we use the following transformation:

(x', y') = (x * cos(theta) - y * sin(theta), x * sin(theta) + y * cos(theta))

In this case, the original point is (-4, 5) and it needs to be rotated 270° counterclockwise.

Let's compute the new coordinates:

x' = -4 * cos(270°) - 5 * sin(270°)
= (-4) * 0 - 5 * (-1) [cos(270°) = 0 and sin(270°) = -1]
= 0 + 5
= 5

y' = -4 * sin(270°) + 5 * cos(270°)
= (-4) * (-1) + 5 * 0 [sin(270°) = -1 and cos(270°) = 0]
= 4 + 0
= 4

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