[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
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
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.
