Question

Use the image to answer the question.A quadrilateral is plotted on a coordinate plane with both the axes ranging from negative 7 to 7.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′.(1 point)E′ is located at (,).

Answer 1

To find the new coordinates of point E(5, 3) after a 90° counterclockwise rotation about the origin, we can use the formula for rotation:

For a point (x, y), the new coordinates (x', y') after a 90° counterclockwise rotation are given by:

\[ (x', y') = (-y, x) \]

Applying this to E(5, 3):

\[ E'(x', y') = (-3, 5) \]

Thus, the coordinates of E' after the rotation are \( E' = (-3, 5) \).

So the answer is:

E′ is located at (-3, 5).