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′

Answer 1

To rotate a point \((x, y)\) by \(90^\circ\) counterclockwise about the origin, you can use the transformation:

\[
(x, y) \to (-y, x)
\]

Now, let's apply this transformation to the point \(E(5, 3)\):

1. **Identify the coordinates of E**: \(E(5, 3)\).
2. **Apply the transformation**:
- New x-coordinate: \(-y = -3\)
- New y-coordinate: \(x = 5\)

Thus, the coordinates of point \(E'\) after the rotation will be:

\[
E'(-3, 5)
\]

Therefore, the coordinate of \(E'\) is \((-3, 5)\).