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. (-3, -4) and (-5, -6) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Find the horizontal and vertical distances

The horizontal distance \(a\) between the \(x -\)coordinates: \(a=\vert-3-(-5)\vert=\vert-3 + 5\vert = 2\)
The vertical distance \(b\) between the \(y -\)coordinates: \(b=\vert-4-(-6)\vert=\vert-4 + 6\vert=2\)

Step2: Apply the Pythagorean theorem

By the Pythagorean theorem \(d=\sqrt{a^{2}+b^{2}}\), where \(d\) is the distance between the two points. Substitute \(a = 2\) and \(b = 2\) into the formula:
\(d=\sqrt{2^{2}+2^{2}}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\)

Answer:

The distance between the two points \((-3,-4)\) and \((-5,-6)\) is \(2\sqrt{2}\)