If A(3, 4), B(7, –2) and C(–2, –1) are the vertices of a ΔABC, write down the equation of the median through the vertex C.

Let median through C be CX.

We know that, the median, CX through C will bisect the line AB.

By Mid-point formula,

Mid-point = $\Big(\dfrac{x$1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

The co-ordinates of point X are

$\Big(\dfrac{3 + 7}{2}, \dfrac{4 + (-2)}{2}\Big) = \Big(\dfrac{10}{2}, \dfrac{2}{2}\Big)$ = (5, 1).

By formula,

Slope = $\dfrac{y$2 - y1}{x2 - x1}

Substituting values we get,

Slope of CX = $\dfrac{1 - (-1)}{5 - (-2)} = \dfrac{2}{7}$.

Then, the required equation of the median CX is given by :

⇒ y - y₁ = m(x - x₁)

⇒ y - (-1) = $\dfrac{2}{7}$[x - (2)]

⇒ 7(y + 1) = 2(x + 2)

⇒ 7y + 7 = 2x + 4

⇒ 7y = 2x + 4 - 7

⇒ 2x - 7y - 3 = 0

Hence, equation of line is 2x - 7y - 3 = 0.