Question 175137: I need help with the following question
Do points P(-2,-2),Q(4,1) and R(2,4) form a right triangle? justify your answer. How can you find the answer by calculation alone?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! in order for this to be a right triangle, one of the sides must be perpendicular to one of the other sides.
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in order for that to happen, the slope of one of the sides must be a negative reciprocal of the slope of one of the other sides.
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slope = (y2-y1)/(x2-x1)
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slope 1 = (1-(-2)/(4-(-2) = 3/6 = 1/2
slope 2 = (4-1)/(2-4) = 3/-2 = -3/2
slope 3 = (4-(-2)/(2-(-2) = 6/4 = 3/2
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a negative reciprocal of 1/2 is -2.
a negative reciprocal of -3/2 = 2/3
a negative reciprocal of 3/2 = -2/3
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none of slopes of these sides match the perpendicular criteria.
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also, if this was a right triangle, then a^2 + b^2 = c^2, with c being the longest side.
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the lengths of each of the sides squared are:
side 1: 3^2 + 6^2 = 9 + 36 = 45
side 2: 6^2 + 4^2 = 36 + 16 = 52
side 3: 3^2 + (-2)^2 = 9 + 4 = 13
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45 + 13 = 58 not equal to 52.
this is not a right triangle.
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i vote no.
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