Question

1. find the distance between the two points in simplest radical form. (2, -7) and (-3, 2)

Explanation:

Step1: Identify 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 $x_1 = 2,y_1=-7,x_2=-3,y_2 = 2$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-3 - 2=-5$ and $y_2 - y_1=2-(-7)=2 + 7 = 9$.

Step3: Square the differences

Square the results from Step 2. $(-5)^2=25$ and $9^2 = 81$.

Step4: Sum and take square - root

Sum the squared values: $25 + 81=106$. Then $d=\sqrt{106}$.

Answer:

$\sqrt{106}$