Question

Ah, this image is a depiction of a polygon over a coordinate plane, offering plenty of room for some geometric exploration! Here's what it features:

Points & Coordinates: The image highlights specific points labeled D, E, F, and G with the coordinates:

D: (1, 4)

E: (6, 4)

F: (7, -1)

G: (1, -1)

Polygon Structure: The points are connected by orange lines to form a quadrilateral. It’s quite symmetrical and likely holds some interesting mathematical properties.

Graph Details: The axes range from -7 to 7 along both the x and y directions, creating a neatly scaled grid for analysis.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 coordinates of the point \( E' \) after a 90° counterclockwise rotation about the origin, we can use the transformation rule for a counterclockwise rotation.

The transformation for a point \( (x, y) \) rotates it to \( (-y, x) \).

Given the coordinates of point \( E \) before the rotation are \( E(5, 3) \):
- After rotation, the coordinates will be:
\[
E' = (-y, x) = (-3, 5)
\]

Therefore, the coordinates of \( E' \) are \( (-3, 5) \).

So, the answer is:
E′ is located at (-3.5)