Question

A(– 4, 2), B(6, 4) and C(2, – 2) are the vertices of $$\triangle \mathrm{ABC}$$. Find the equation of median AD.

Answer 1

$$\mathrm{D}$$ is the mid-point of $$\mathrm{BC}$$: 

$$\mathrm{D} = \left(\frac{6 + 2}{2}, \frac{4 + (-2)}{2}\right) = (4, 1)$$ 

Slope of median $$\mathrm{AD}$$ joining $$\mathrm{A}(-4, 2)$$ and $$\mathrm{D}(4, 1)$$: 

$$m_{\mathrm{AD}} = \frac{1 - 2}{4 - (-4)}$$

$$= \frac{-1}{8}$$

$$= -\frac{1}{8}$$

Equation of median $$\mathrm{AD}$$: 

$$y - 1 = -\frac{1}{8}(x - 4)$$

$$8(y - 1) = -(x - 4)$$

$$8y - 8 = -x + 4$$

$$x + 8y - 12 = 0$$