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?
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).