The coordinates of the vertices of ∆pqr are p(-2,5), q(-1,1), and r(7,3). determine whether ∆pqr is a right triangle. show your work and explain your answer!

Step 1

Plot the vertices of triangle PQR

using a graphing tool

see the attached figure

we know that the distance between two points is equal to

Step 2

Find the distance PR

substitute the values

Step 3

Find the distance QP

substitute the values

Step 4

Find the distance QR

substitute the values

Step 5

If triang;le PQR is a right triangle

then

Applying the Pythagorean Theorem

substitute the values

---------> is true

therefore

The answer is

The triangle PQR is a right triangle

the answer to the question is a  

it has the same slope and the same y-intercept.