SOLUTION: Analytic Geometry 1.a) Draw the triangle with vertices P(-2,-2), Q(2,4), and R(8,0). b) Show algebraically that PQR is a right triangle. c) Is PQR also an isosceles triangle?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Analytic Geometry 1.a) Draw the triangle with vertices P(-2,-2), Q(2,4), and R(8,0). b) Show algebraically that PQR is a right triangle. c) Is PQR also an isosceles triangle?       Log On


   

Question 177793: Analytic Geometry
1.a) Draw the triangle with vertices P(-2,-2), Q(2,4), and R(8,0).
b) Show algebraically that PQR is a right triangle.
c) Is PQR also an isosceles triangle?
Use algebraic reasoning to justify your answer.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a.)
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b.) You can use the Pythagoran theorem to check if PQR is a right triangle.
PQ%5E2%2BQR%5E2=PR%5E2
Using the distance formula to calculate line segment lengths,
D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2
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PQ%5E2=%28-2-2%29%5E2%2B%28-2-4%29%5E2
PQ%5E2=%28-4%29%5E2%2B%28-6%29%5E2
PQ%5E2=16%2B36
PQ%5E2=52
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QR%5E2=%282-8%29%5E2%2B%284-0%29%5E2
QR%5E2=36%2B16
QR%5E2=52
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PR%5E2=%28-2-8%29%5E2%2B%28-2-0%29%5E2
PR%5E2=%28-10%29%5E2%2B%28-2%29%5E2
PR%5E2=100%2B4
PR%5E2=104
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PQ%5E2%2BQR%5E2=PR%5E2
52%2B52=104
104=104
Since the two sides are equal, the Pythagorean theorem holds and PQR is a right triangle.
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c.) The legs of an isoceles triangle are congruent.
Since PQ%5E2=QR%5E2, then PQ=QR so this right triangle is also an isoceles triangle.