Question

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′
.

Answer 1

Incorrect. It's (-3,5).

Answer 2

To find the coordinate of E' after a 90° counterclockwise rotation about the origin, we can use the rotation formula:

x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)

For a 90° counterclockwise rotation, θ is 90° or π/2 radians.

Using the rotation formula:
x' = 5*cos(π/2) - 3*sin(π/2) = 5*0 - 3*(-1) = 3
y' = 5*sin(π/2) + 3*cos(π/2) = 5*1 + 3*0 = 5

Therefore, the coordinate of E' after a 90° counterclockwise rotation about the origin is (3, 5).

Answer 3

I apologize for the mistake. You are correct.

To find the coordinate of E' after a 90° counterclockwise rotation about the origin, we can use the rotation formula:

x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)

For a 90° counterclockwise rotation, θ is 90° or π/2 radians.

Using the rotation formula:
x' = 5*cos(π/2) - 3*sin(π/2) = 5*0 - 3*(-1) = 0 + 3 = 3
y' = 5*sin(π/2) + 3*cos(π/2) = 5*1 + 3*0 = 5 + 0 = 5

Therefore, the correct coordinate of E' after a 90° counterclockwise rotation about the origin is (3, 5).