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 after a 90° counterclockwise rotation about the origin, you can use the rotation transformation rules. For a point \((x, y)\), after a 90° counterclockwise rotation, the new coordinates \((x', y')\) will be:

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

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

1. For the x-coordinate:
\[
x' = -y = -3
\]

2. For the y-coordinate:
\[
y' = x = 5
\]

Therefore, the coordinates of \(E'\) after the rotation will be \((-3, 5)\).

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

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