Question

1. find the distance between the two points in simplest radical form. (-5,0) and (-9,9)

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign the values of the points

Let $(x_1,y_1)=(-5,0)$ and $(x_2,y_2)=(-9,9)$. Then $x_2 - x_1=-9-(-5)=-9 + 5=-4$ and $y_2 - y_1=9 - 0 = 9$.

Step3: Substitute into the formula

$d=\sqrt{(-4)^2+9^2}=\sqrt{16 + 81}$.

Step4: Simplify the expression

$d=\sqrt{97}$.

Answer:

$\sqrt{97}$