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.
(6, -5) and (-3, 7)
click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(6, - 5)$ and $(x_2,y_2)=(-3,7)$.

Step2: Apply the 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: $x_2 - x_1=-3 - 6=-9$ and $y_2 - y_1=7-( - 5)=7 + 5 = 12$.
Then $d=\sqrt{(-9)^2+12^2}$.

Step3: Calculate the squares and sum

$(-9)^2 = 81$ and $12^2=144$. So $(-9)^2+12^2=81 + 144=225$.
Then $d=\sqrt{225}$.

Step4: Simplify the square - root

$\sqrt{225}=\sqrt{15\times15}=15$.

Answer:

$15$