SOLUTION: Use coordinate geometry to prove that triangle PQR is isosceles... ^ | |---------Q (a,b) | | | | | P(0,0)----------- -R(2a,0) ----------- ----------- ------>

Algebra ->  Geometry-proofs -> SOLUTION: Use coordinate geometry to prove that triangle PQR is isosceles... ^ | |---------Q (a,b) | | | | | P(0,0)----------- -R(2a,0) ----------- ----------- ------>      Log On


   

Question 936288: Use coordinate geometry to prove that triangle PQR is isosceles...
^
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|---------Q (a,b)
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|
|
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| P(0,0)-------------R(2a,0)
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Answer by hovuquocan1997(83) About Me  (Show Source):
You can put this solution on YOUR website!
We have the distance formula is d=sqrt%28%28y1-y2%29%5E2%2B%28x1-x2%29%5E2%29
So first, we find the distance between P and Q
d=sqrt%28%28b-0%29%5E2%2B%28a-0%29%5E2%29
d=sqrt%28b%5E2%2Ba%5E2%29
Then, we find the distance between Q and R
d=sqrt%28%28b-0%29%5E2%2B%28a-2a%29%5E2%29
d=sqrt%28b%5E2%2B%28-a%29%5E2%29
d=sqrt%28b%5E2%2Ba%5E2%29 (because %28-a%29%5E2=a%5E2
We can see that the two distance are the same, so we can conclude that PQ=QR
A triangle that has two equal sides is isosceles.
:D