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Question 249136: Decided weather or not the points are vertices of a right triangle: (-3,8) (3,10) (7,-2)
Answer by actuary(112)   (Show Source):
You can put this solution on YOUR website! Using the distance formula, fund the length of each of the 3 ides of the triangle,
Length of side 1 --- Square Root of [(3-(-3))^2+(10-8)^2]=Square Root of [6^2+2^2]=Square Root of 40.
Length of Side 2 --- Square Root of [7-3)^2+(-2-10)^2]=Square Root of [4^2+(-12)^2]=Square Root of [16+144] =Square Root of 160.
Length of Side 3 --- Square Root of [-3-7)^2+(8-(-2))^2]=Square Root of [(-10)^2+(8+2)^2]=Square Root of [100+100] =Square Root of 200.
Since the length of side 3 is the largest it must be the hypoteneuse of the right triangle if the triangle is to be a right triangle. For the triangle to be a right triangle, the Pythagorean Theorem has to be met so that
200^2 must be equal 160^2 + 40^2. In other words, 200^2=40^2+160^2. But this isn't true, so the triangle is NOT a right triangle.
The problem is an attempt to get you to show that something isn't true by using facts that must be true if the original statement was true.
Have fun studying math.
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