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?(1 point)
To rotate a point counterclockwise about the origin, we can use the following formulas:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
In this case, the point is (-4, 5) and we want to rotate it 270 degrees counterclockwise.
Using the formulas, we can substitute the values into the equations:
x' = -4 * cos(270) - 5 * sin(270)
y' = -4 * sin(270) + 5 * cos(270)
Now, we can substitute the values of sin(270) = -1 and cos(270) = 0:
x' = -4 * 0 - 5 * (-1)
y' = -4 * (-1) + 5 * 0
Simplifying, we get:
x' = 0 + 5 = 5
y' = 4 + 0 = 4
Therefore, the new point after rotating counterclockwise about the origin 270 degrees is (5, 4).