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Question 1021353: http://prntscr.com/a5xl25
Coordinate geometry.
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?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! midpoint of a line is equal to ((x1+x2)/2,(y1+y1)/2)
(x1,y1) = -a,0
(x,y2) = a,0
midpoint is ((a-a)/2,(0-0)/2 = (0,0)
the median intersect the horizontal line of the triangle at (0,0).
the slope of the horizontal line is 0.
slope = (y2-y1) / (x2-x1) = (0-0) / (a-(-a)) = 0 / (2a) = 0.
the slope of the median is (y2-y1) / (x2-x1) = (b-0) / (0-0) = b/0 = undefined.
this makes the median a vertical line.
vertical lines and horizontal lines are perpendicular to each other.
if the slope is 0, the line is horizontal.
if the slope is undefined the line is vertical.
the median is therefore perpendicular to the base of the triangle.
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