SOLUTION: Please help me! Triangle ABC is formed by the points A(2,0), B(4,-4) and C(-2,-2). Prove using a property of linear relations that this is a right triangle.

Question 1140964: Please help me!
Triangle ABC is formed by the points A(2,0), B(4,-4) and C(-2,-2). Prove using a property of
linear relations that this is a right triangle.
Found 2 solutions by Boreal, rothauserc:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Look at the slopes of any two of the points and see if they are a negative reciprocal, which would mean perpendicular
AB has slope of -4/2
BC has slope of 2/-6 or -1/3
CA has slope of -2/-4 or +1/2
AB and CA have a negative reciprocal slope so perpendicular.
One can also use the distance formula for
AB sqrt(4+16)
BC sqrt (36+4)
CA sqrt (4+16)
sum of the sqrts is 20+20=40, and that is a right triangle as well.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
A linear relation is a relation that forms a straight line.
:
In a right triangle, two line segments are perpendicular(right angle) to each other if their slopes are the negative reciprocal of each other
:
slope of line segment AB = (-4 -0)/(4 -2) = -2
:
slope of line segment BC = (-2 -(-4))/(-2 -4) = -1/3
:
slope of line segment CA = (0 -(-2))/(2 -(-2)) = 1/2
:
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line segments AB and CA are perpendicular to each other, therefore triangle ABC is a right triangle
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