Question

Find the distance between the two points in simplest radical form. (6,6) (3,9)

Answer 1

Answer:

$3\sqrt{2}$ units

Step-by-step explanation:

To find the distance between two points on a graph, we use the distance formula $d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2$ where $d$ is the distance between points $(x_1,y_1)$ and $(x_2,y_2)$.

For this problem, we will identify $(x_1,y_1)\rightarrow(6,6)$ and $(x_2,y_2)\rightarrow(3,9)$:

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\d=\sqrt{(9-6)^2+(3-6)^2}\\\\d=\sqrt{(3)^2+(-3)^2}\\\\d=\sqrt{9+9}\\\\d=\sqrt{18}\\\\d=3\sqrt{2}$

Therefore, the distance between $(6,6)$ and $(3,9)$ is $3\sqrt{2}$ units