rotate the point (2, 4) on a geometric figure 270° clockwise. What is the new point?
a. (-4, 2)
b. (4, -2)
c. (-4, -2)
d. (-2, -4)
To rotate a point (x, y) 270° clockwise, we can apply the following transformation:
x' = x * cos(270°) - y * sin(270°)
y' = x * sin(270°) + y * cos(270°)
Since cos(270°) = 0 and sin(270°) = -1, we can simplify the equations:
x' = x * 0 - y * (-1)
y' = x * (-1) + y * 0
x' = y
y' = -x
Plugging in the given point (2, 4):
x' = 4
y' = -2
Therefore, the new point is (4, -2), which corresponds to option b.