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Question 1022026: http://prntscr.com/a5xl25
So, I know I have to use the distance formula, and the points I need to work with are (-a, 0) & (a,0) and the median of the triangle (0,0) & (0,b). However, I'm not sure how to simplify these variables in the distance formula. Can you help step by step? Don't use the midpoint formula please. Please only explain and show me with the distance formula. Also, it's not plugging the variables into the distance formula I'm having trouble with. It's simplifying the distance formula and using the answer from the distance formula after I solve it to prove the lines are perpendicular that I'm having trouble with.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! looks like this is an isosceles triangle but let's use the distance formula to determine the length of each side.
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d1 = square root( (0-(-a))^2 + (b - 0)^2 ) = square root( a^2 + b^2)
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d2 = square root( (0-a)^2 + (b-0)^2 ) = square root( a^2 + b^2)
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d3 = square root( (a-(-a))^2 +(0-0)^2 ) = square root( (2a)^2)
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d1 = d2, so we do have an isosceles triangle
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d1 and d2 are adjacent sides, so the median bisects the angle between them and also bisects the base of the triangle
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let D be the point of intersection on the base with the median
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the two triangles are congruent by SAS
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the two angles on ether side of the median at D are co-linear (they sum to 180 degrees) and they are equal because of congruence
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therefore the median is perpendicular at D
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