Question

Find a point P which divides internally the line segment joining the points A(–3, 9) and B(1, –3) in the ratio 1 : 3.

Answer 1

Here $$m : n = 1 : 3$$, $$A(-3, 9)$$ and $$B(1, -3)$$.

$$x = \frac{1\times 1 + 3 \times (-3)}{1 + 3}$$

$$= \frac{1 - 9}{4}$$

$$= \frac{-8}{4}$$

$$= -2$$

$$y = \frac{1 \times (-3) + 3 \times 9}{1 + 3}$$

$$= \frac{-3 + 27}{4}$$

$$= \frac{24}{4}$$ 

$$= 6$$

Hence the required point is $$P(-2, 6)$$.