Question

Figure ABCD is rotated 90°counterclockwise about the origin. Which of the following gives the correct measure of an image of one of its sides?

B'C' = √17
C'D' = √10
D'D' = 5
A'B' = √17

Answer 1

its your last option or A'B'=17

Answer 2

Answer:

The correct option is 4.

Step-by-step explanation:

90°counterclockwise about the origin is a rigid transformation. It means the measure of corresponding sides of image and preimage are same.

$AB=A'B',BC=B'C',CD=C'D',AD=A'D'$

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The measure of all sides are

$AB=A'B'=\sqrt{(4-0)^2+(-3+4)^2}=\sqrt{17}$

$BC=B'C'=\sqrt{(5-4)^2+(-6+3)^2}=\sqrt{10}$

$CD=C'D'=\sqrt{(1-5)^2+(-7+6)^2}=\sqrt{17}$

$AD=A'D'=\sqrt{(1-0)^2+(-7+4)^2}=\sqrt{10}$

Since A'B' = √17 gives the correct measure of an image of one of its sides, therefore correct option is 4.