Question

016.
Triangle ABC is an isosceles triangle with AB = AC and vertex A is on y-axis. If the coordinates of vertex B and C are (-5, -2) and (3, 2) respectively, then find the coordinates of vertex A. Also, find the
length of median AD.
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Answer 1

Draw perpendicular from A to BC

As it will bisect BC because its isosceles

So its perpendicular bisector

BC slope = ( 2+2)/(3+5) = 4/8 = 1/2

Slope of AD = -2

AS pass throughD mid point of BC( -5+3/2, 2-2/2 = (-1,0)

and A( 0,a) its on y axis

So ( a-0)/(0-(-1)) = -2

a = -2

So point A is (0,-2)

Length AD = √4 + 1 = √5