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 \((-3, 5)\).