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. (-9, -4) and (-2, 2) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Find the difference in x - coordinates

Let $(x_1,y_1)=(-9,-4)$ and $(x_2,y_2)=(-2,2)$. The difference in x - coordinates $\Delta x=x_2 - x_1=-2-(-9)=7$.

Step2: Find the difference in y - coordinates

The difference in y - coordinates $\Delta y=y_2 - y_1=2-(-4)=6$.

Step3: Use the distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substituting $\Delta x = 7$ and $\Delta y = 6$ into the formula, we get $d=\sqrt{7^{2}+6^{2}}=\sqrt{49 + 36}=\sqrt{85}$.

Answer:

$\sqrt{85}$