Question

1. find the distance between the two points in simplest radical form. (-6, -9) and (-6, -6)

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 $x_1=-6,y_1 = - 9,x_2=-6,y_2=-6$.

Step2: Substitute values

Substitute the values into the formula: $d=\sqrt{(-6-(-6))^2+(-6 - (-9))^2}=\sqrt{( - 6 + 6)^2+(-6 + 9)^2}$.

Step3: Simplify

First, $-6 + 6=0$ and $-6 + 9 = 3$. So $d=\sqrt{0^2+3^2}=\sqrt{0 + 9}=\sqrt{9}=3$.

Answer:

$3$