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.

Let r = the distance from P(-2,-4) to Q(-4,-2); 
r = √{(-4 - -2)² + (-2 - -4)²} 
r = √{-2² + 2²} 
r = √{4 + 4} 
r = √8 
Let q = the distance from P(-2,-4) to R(7,-1): 
q = √{(7 - -2)² + (-1 - -4)²} 
q = √{9² + 3²} 
q = √{81 + 9} 
q = √90 
Let p = the distance from Q(-4,-2) to R(7,-1): 
p = √{(7 - -4)² + (-1 - -2)²} 
p = √{11² + 1²} 
p = √{121 + 1) 
p = √122 
If PQR is a right triangle, then: 
p² = q² + r² 
122 = 90 + 8 
122 ≠ 98 
Therefore, it is not a right triangle.

3937.5 should be your answer