Question

A(1, −5), B(2, 2) and C(−2, 4) are the vertices of triangle ABC. Find the equation of the median of the triangle through A.

Answer 1

We know the median through A will pass through the mid-point of BC.

Let AD be the median through A.

Co-ordinates of the mid-point of BC, i.e., D are

${\displaystyle (\frac{2-2}{2},\frac{2+4}{2})}$

= ${\displaystyle (\frac{0}{2},\frac{6}{2})}$

= (0, 3)

Slope of AD = ${\displaystyle \frac{3+5}{0-1}=-8}$

Equation of the median AD is

y – 3 = –8(x – 0)

8x + y = 3