Question

P(3, 4), Q(7, –2) and R(–2, –1) are the vertices of triangle PQR. Write down the equation of the median of the triangle through R.

Answer 1

Let median through R be RX.

We know that, the median, RX through R will bisect the line PQ.

By Mid-point formula,

Mid-point = `((x_1 + x_2)/2, (y_1 + y_2)/2)`

The co-ordinates of point X are

`((3 + 7)/2, (4 +(-2))/2)`

= `(10/2, 2/2)`

= (5, 1)

By formula,

Slope = `(y_2 - y_1)/(x_2 - x_1)`

Substituting values we get,

Slope of RX = `(1 - (-1))/(5 - (-2)) = 2/7`

Then, the required equation of the median RX is given by

`=>` y − y₁ = m(x − x₁)

`=> y - (-1) = 2/7[x - (-2)]`

`=> y + 1 = 2/7(x + 2)`

`=>` 7(y + 1) = 2(x + 2)

`=>` 7y + 7 = 2x + 4

`=>` 7y = 2x – 3

Hence, equation of the median through R is 7y = 2x – 3.