Question

1. point d is rotated about point e. find the length of $overline{ed}$

$d(-6, -5)$
$e(-3, 1)$

Explanation:

Step1: Recall distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, for points $E(-3,1)$ and $D(-6,-5)$, let $(x_1,y_1)=(-3,1)$ and $(x_2,y_2)=(-6,-5)$.

Step2: Substitute values into formula

$ED=\sqrt{(-6 - (-3))^2+(-5 - 1)^2}=\sqrt{(-6 + 3)^2+(-6)^2}=\sqrt{(-3)^2+(-6)^2}=\sqrt{9 + 36}=\sqrt{45}=3\sqrt{5}$. Since rotation does not change the distance between two points, $ED'=ED$.

Answer:

$3\sqrt{5}$