Question

Trapezoid \(DEFG\) has vertices \(D\left(1,3\right)\), \(E\left(5,3\right)\), \(F\left(7,-1\right)\) and \(G\left(1,-1\right)\). Imagine the image \(D'E'F'G'\) after a \(90\degree\) (counterclockwise) rotation about the origin. Enter the coordinate of \(E'\).

(1 point)
\(E'\) is located at (
,
).

Answer 1

To rotate a point \((x, y)\) counterclockwise by \(90^\degree\) around the origin, the new coordinates \((x', y')\) can be determined using the transformation:

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

Now, applying this transformation to point \(E(5, 3)\):

- The original coordinates are \(x = 5\) and \(y = 3\).

Using the formula:

\[
x' = -y = -3
\]
\[
y' = x = 5
\]

Thus, the new coordinates for point \(E'\) after the rotation are:

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

Therefore, the coordinates of \(E'\) are:

\[
E' \text{ is located at } (-3, 5).
\]