Question 1021353
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.