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, -4) and (-5, -6) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Identify coordinates

Let $(x_1,y_1)=(-3,-4)$ and $(x_2,y_2)=(-5,-6)$.

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: $x_2 - x_1=-5-(-3)=-2$, $y_2 - y_1=-6 - (-4)=-2$. Then $d=\sqrt{(-2)^2+(-2)^2}$.

Step3: Simplify the expression

$(-2)^2 = 4$, so $d=\sqrt{4 + 4}=\sqrt{8}$. Simplify $\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$.

Answer:

$2\sqrt{2}$