Question

1. graph a right triangle with the points (-7, -2) and (-5, -9) and find the hypotenuse. using the sides, find the distance between the two points in simplest radical form. leg 1: __ leg 2: hypotenuse: __

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, let $(x_1,y_1)=(-7,-2)$ and $(x_2,y_2)=(-5,-9)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-5-(-7)=-5 + 7 = 2$, $y_2 - y_1=-9-(-2)=-9 + 2=-7$.

Step3: Substitute into formula

Substitute into the distance formula: $d=\sqrt{(2)^2+(-7)^2}=\sqrt{4 + 49}=\sqrt{53}$.
For the legs of the right - triangle formed:
The horizontal leg (difference in x - coordinates) is $|x_2 - x_1| = 2$.
The vertical leg (difference in y - coordinates) is $|y_2 - y_1|=7$.

Answer:

Leg 1: 2
Leg 2: 7
Hypotenuse: $\sqrt{53}$