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. (5, -6) and (-4, 1) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Find horizontal and vertical distances

Let $(x_1,y_1)=(5, - 6)$ and $(x_2,y_2)=(-4,1)$. The horizontal distance $a=\vert x_2 - x_1\vert=\vert-4 - 5\vert = 9$. The vertical distance $b=\vert y_2 - y_1\vert=\vert1-(-6)\vert=7$.

Step2: Apply the Pythagorean theorem

The distance $d$ between two points is the length of the hypotenuse of the right - triangle. By the Pythagorean theorem $d=\sqrt{a^{2}+b^{2}}=\sqrt{9^{2}+7^{2}}=\sqrt{81 + 49}=\sqrt{130}$.

Answer:

$\sqrt{130}$