Question

question
find the distance between the two points in simplest radical form.

Explanation:

Step1: Identify the two points

The points are $(-2, 6)$ and $(7, 3)$.

Step2: Recall distance formula

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

Step3: Substitute values into formula

$d=\sqrt{(7-(-2))^2+(3-6)^2}=\sqrt{(9)^2+(-3)^2}$

Step4: Calculate squared terms

$d=\sqrt{81+9}$

Step5: Simplify the radical

$d=\sqrt{90}=\sqrt{9\times10}=3\sqrt{10}$

Answer:

$3\sqrt{10}$