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
To rotate a point counterclockwise about the origin, we use the formula:
(x', y') = (x*cos(θ) - y*sin(θ), x*sin(θ) + y*cos(θ))
Where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the rotated point, and θ is the angle of rotation.
In this case, the original point is (-4, 5), and we want to rotate it counterclockwise 270 degrees.
Plugging the values into the formula:
(x', y') = (-4*cos(270°) - 5*sin(270°), -4*sin(270°) + 5*cos(270°))
Now, we need to calculate the trigonometric functions of 270°.
cos(270°) = 0
sin(270°) = -1
Plugging these values back into the formula:
(x', y') = (-4*0 - 5*(-1), -4*(-1) + 5*0)
(x', y') = (0 + 5, 4 + 0)
(x', y') = (5, 4)
Therefore, the new point when (-4, 5) is rotated counterclockwise about the origin by 270 degrees is (5, 4).