Question

find the distance between the two points in simplest radical form. (6,9) and (-3,7)

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, $x_1 = 6,y_1=9,x_2=-3,y_2 = 7$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-3 - 6=-9$, $y_2 - y_1=7 - 9=-2$.

Step3: Square the differences

Square the results from step 2. $(-9)^2 = 81$ and $(-2)^2=4$.

Step4: Sum the squared - differences

Add the squared values: $81 + 4=85$.

Step5: Take the square - root

$d=\sqrt{85}$.

Answer:

$\sqrt{85}$