Question

If A(3, 4), B(7, –2) and C(–2, –1) are the vertices of a $$\triangle \mathrm{ABC}$$, write down the equation of the median through the vertex C.

Answer 1

The median through vertex $$C$$ connects $$C$$ to the mid-point of $$AB$$, say $$D$$.

Coordinates of $$D$$: 

$$D = \left(\frac{3 + 7}{2}, \frac{4 + (-2)}{2}\right)$$

$$= \left(\frac{10}{2}, \frac{2}{2}\right)$$

$$= (5, 1)$$

Slope of median $$CD$$ where $$C(-2, -1)$$ and $$D(5, 1)$$:

$$m = \frac{1 - (-1)}{5 - (-2)}$$

$$= \frac{2}{7}$$

Equation of median $$CD$$:

$$y - 1 = \frac{2}{7}(x - 5)$$

$$7(y - 1) = 2(x - 5)$$

$$7y - 7 = 2x - 10$$

$$2x - 7y - 3 = 0$$