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.

Answer 1

Explanation:

Given the points:

`(7,-5)\text{ and }(2,-7)`

The graphed right triangle is given below:

Using the sides, we then find the distance between the two points, d.

By the Pythagorean theorem:

`\begin{gathered} d^2=[5-(-7)]^2+[7-2]^2 \\ d^2=[5+7]^2+5^2 \\ d^2=12^2+5^2 \\ d^2=144+25 \\ d^2=169 \\ d^2=13^2 \\ \implies d=13 \end{gathered}`

The distance between the two poi