Question

In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (–2, 3) and (0, 1) respectively. Find the equation of median through vertex A. Also, find the equation of the line through vertex B and parallel to AC.

Answer 1

Given, the co-ordinates of vertices A, B and C of a triangle ABC are (4, 7), (–2, 3) and (0, 1) respectively.

Let AD be the median through vertex A.

Co-ordinates of the point D are

`((-2 + 0)/2, (3 + 1)/2)`

(–1, 2)

∴ Slope of AD = `(2 - 7)/(-1 - 4) = (-5)/(-5) = 1`

The equation of the median AD is given by:

y − y₁ = m(x − x₁)

y − 2 = 1(x + 1)

y − 2 = x + 1

y = x + 3

The slope of the line which is parallel to line AC will be equal to the slope of AC.

Slope of AC = `(1 - 7)/(0 - 4) = (-6)/(-4) = 3/2`

The equation of the line which is parallel to AC and passes through B is given by:

`y - 3 = 3/2(x + 2)`

2y − 6 = 3x + 6

2y = 3x + 12