SOLUTION: how that the triangle whose vertice are p(2,-2) Q(-4,-5) and R(8,9) is isosceles

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Question 884328: how that the triangle whose vertice are p(2,-2) Q(-4,-5) and R(8,9) is isosceles
Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
Well if your asking if that triangle is isosceles then you need to determine if all three sides are the same length, since for a triangle to be isosceles it needs to have all 3 sides the same length. Which means finding the distance between P and Q, P and R, and Q and R.

To find the distance between two points we use the distance formula which is d=sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29.

Now lets try finding the distance between P and Q. P(2,-2) and Q(-4,5) from above and now we plug and chug:

d=sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29
=d=sqrt%28%28-4-2%29%5E2%2B%28-5-%28-2%29%29%5E2%29
=d=sqrt%28%28-6%29%5E2%2B%28-3%29%5E2%29
=d=sqrt%2836%2B9%29
=d=sqrt%2845%29
=d=3sqrt%285%29

Now lets try finding the distance between P and R. P(2,-2) and R(8,9) so we plug and chug again.
d=sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29
=d=sqrt%28%288-2%29%5E2%2B%289%2B2%29%5E2%29
=d=sqrt%28%286%29%5E2%2B%2811%29%5E2%29
=d=sqrt%2836%2B121%29
=d=sqrt%28157%29

Since sqrt%28157%29 is not the same as 3sqrt%285%29 then the triangle is not isosceles.