Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points in simplest radical form. (3,8) and (6,2) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Identify coordinates

Let $(x_1,y_1)=(3,8)$ and $(x_2,y_2)=(6,2)$.

Step2: Apply distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute the values: $x_2 - x_1=6 - 3 = 3$ and $y_2 - y_1=2 - 8=-6$. Then $d=\sqrt{3^2+( - 6)^2}$.

Step3: Calculate squares and sum

$3^2 = 9$ and $(-6)^2=36$. So $d=\sqrt{9 + 36}=\sqrt{45}$.

Step4: Simplify radical

$\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}$.

Answer:

$3\sqrt{5}$