Trapezoid DEFG

Question

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

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

For the point E(5, 3):

• The x-coordinate is 5 and the y-coordinate is 3.
• Applying the formula:

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

Thus, the coordinates of E' after the rotation are:

\[ E'(−3, 5) \]

So, the coordinate of E′ is \((-3, 5)\).