SOLUTION: The coordinates of the vertices of ∆PQR are P (0,4), Q (4,0), and R (8,4) Determine whether ∆PQR is a right triangle. Show all work. Using distance determine if the trian

Algebra ->  Triangles -> SOLUTION: The coordinates of the vertices of ∆PQR are P (0,4), Q (4,0), and R (8,4) Determine whether ∆PQR is a right triangle. Show all work. Using distance determine if the trian      Log On


   



Question 1149553: The coordinates of the vertices of ∆PQR are P (0,4), Q (4,0), and R (8,4)
Determine whether ∆PQR is a right triangle. Show all work.
Using distance determine if the triangle is an isosceles triangle. Show all work.

Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The coordinates of the vertices of ∆PQR are P (0,4), Q (4,0), and R (8,4)
Determine whether ∆PQR is a right triangle.
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Find the lengths of the 3 sides, a, b & c.
Call the longest side c.
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If c^2 = a^2 + b^2 it's a right triangle.

Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
system%28PQ=16%2Asqrt%282%29%2CQR=16%2Asqrt%282%29%2CRP=8%29
Isosceles because PQ and QR are congruent.

Slopes:
PQ, -1
QR, 1
RP, ...

Notice two of them are negative reciprocal of each other.