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, -7) and (3, -4) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Identify coordinates

Let $(x_1,y_1)=(-6,-7)$ and $(x_2,y_2)=(3,-4)$.

Step2: Calculate horizontal and vertical distances

The horizontal distance $\Delta x=x_2 - x_1=3-(-6)=9$. The vertical distance $\Delta y=y_2 - y_1=-4 - (-7)=3$.

Step3: Apply distance formula

By the distance formula $d = \sqrt{(\Delta x)^2+(\Delta y)^2}$, we substitute $\Delta x = 9$ and $\Delta y=3$. So $d=\sqrt{9^{2}+3^{2}}=\sqrt{81 + 9}=\sqrt{90}$.

Step4: Simplify the radical

$\sqrt{90}=\sqrt{9\times10}=3\sqrt{10}$.

Answer:

$3\sqrt{10}$