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[1] The median to the base passes through the top point (0,b) and the bottom point (0,0) since it is going straight down. The slope formula is
So, the slope of the median is (b-0)/(0-0) = b/0. Technically, this is undefined, but let's leave it this way for now.
[2] The base passes through the left point (-a,0) and the right point (a,0). Its slope must be (0-0)/(a-(-a)) = 0.
[3] We now check if the slopes are negative reciprocals. Flipping b/0 over and putting a negative sign gives:
b/0 -> - 0/b = 0
So the slopes are negative reciprocals, which means the lines are perpendicular.
So, the slope of the median is (b-0)/(0-0) = b/0. Technically, this is undefined, but let's leave it this way for now.
[2] The base passes through the left point (-a,0) and the right point (a,0). Its slope must be (0-0)/(a-(-a)) = 0.
[3] We now check if the slopes are negative reciprocals. Flipping b/0 over and putting a negative sign gives:
b/0 -> - 0/b = 0
So the slopes are negative reciprocals, which means the lines are perpendicular.
