Final answer:
To rotate a point E(-4,5) 270 degrees, we can use the rotation formula x' = xcos(theta) - ysin(theta) and y' = xsin(theta) + ycos(theta). Applying this formula, the coordinates of point E after rotating are (5,4).
Step-by-step explanation:
To rotate a point in the coordinate plane, we can use the rotation formula:
x' = xcos(theta) - ysin(theta)
y' = xsin(theta) + ycos(theta)
Applying this formula to point E(-4,5) and rotating it 270 degrees, we have:
x' = -4cos(270) - 5sin(270)
y' = -4sin(270) + 5cos(270)
Calculating the values, we get:
x' = -4(0) - 5(-1)
y' = -4(-1) + 5(0)
x' = 5
y' = 4
Therefore, after rotating the image 270 degrees, the coordinates of point E are (5,4).