Question

1. find the distance between the two points in simplest radical form. (-8, -9)and (-6, -5)

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, $x_1=-8,y_1 = - 9,x_2=-6,y_2=-5$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-6-(-8)=2$, $y_2 - y_1=-5-(-9)=4$.

Step3: Substitute into formula

Substitute into the distance formula: $d=\sqrt{(2)^2+(4)^2}=\sqrt{4 + 16}$.

Step4: Simplify

$\sqrt{4 + 16}=\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$.

Answer:

$2\sqrt{5}$