Question

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 horizontal and vertical distances

For the \(x -\)coordinates: \(\vert-2-(-9)\vert=\vert-2 + 9\vert=7\)
For the \(y -\)coordinates: \(\vert2-(-4)\vert=\vert2 + 4\vert=6\)

Step2: Apply the Pythagorean theorem

Let \(a = 7\) and \(b = 6\). By the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the distance between the two points.

$$c=\sqrt{7^{2}+6^{2}}=\sqrt{49 + 36}=\sqrt{85}$$

Answer:

\(\sqrt{85}\)