Question

Give 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 find the new point when the given point is rotated counterclockwise about the origin, we can use the rotation formulas.

Given the point (-4, 5), we need to rotate it counterclockwise about the origin by 270 degrees.

The rotation formula in the standard Cartesian coordinate system is:

x' = x*cosθ - y*sinθ
y' = x*sinθ + y*cosθ

where (x, y) is the original point, (x', y') is the new point, and θ is the angle of rotation.

Substituting the values into the formulas:

x' = (-4)*cos(270°) - 5*sin(270°)
y' = (-4)*sin(270°) + 5*cos(270°)

Using trigonometric identities, cos(270°) = 0 and sin(270°) = -1, so the formulas become:

x' = (-4)*0 - 5*(-1)
y' = (-4)*(-1) + 5*0

Simplifying:

x' = 0 + 5 = 5
y' = 4 + 0 = 4

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