Show that Triangle NPQ is a right triangle. Show work algebraically and explain how the steps in your work shows that Triangle NPQ is a right triangle

Question

Points of Triangle NPQ

N (-14, -1)
P (10, -3)
Q (6, 7)

Answer 1

slope = m = (y₂-y₁)/x₂-x₁)

m_NQ = (7+1)/(6+14) = 2/5   and m_QP = (7+3)/6-10) = -5/2

Since the slopes are negative reciprocals, NQ⊥QP.

BTW, the lengths do not have to be 3, 4, and 5.

 

Answer 2

Find the slope between N and P

  "     "          "             P and Q

  "     "          "             Q and N

 

 

If one slope is the negative reciprocal of any of the other two slopes, then you have a right triangle.  Also, the distance NP, PQ, and QN must have the lengths 3, 4, and 5.