Question

Trapezoid DEFG has vertices D(1,3), E(5,3), F(7,−1) and G(1,−1). Imagine the image D′E′F′G′ after a 90° (counterclockwise) rotation about the origin. Enter the coordinate of E′.

E′ is located at (_,_).

Answer 1

To find the coordinates of point \( E' \) after a 90-degree counterclockwise rotation about the origin, we can use the rotation transformation formula:

For any point \( (x, y) \):
- After a 90-degree counterclockwise rotation, the new coordinates \( (x', y') \) are given by:
\[
(x', y') = (-y, x)
\]

Given the coordinates of point \( E \) are \( (5, 3) \):

1. Apply the rotation formula:
- New x-coordinate: \( x' = -y = -3 \)
- New y-coordinate: \( y' = x = 5 \)

So, the coordinates of \( E' \) after the rotation are:
\[
E' = (-3, 5)
\]

Therefore, E′ is located at \((-3, 5)\).