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).
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?
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