Question

The point \(\mathrm{P}(-4, 1)\) divides the line segment joining the points \(\mathrm{A}(2, -2)\) and B in the ratio 3 : 5. Find the co-ordinates of point B.

Answer 1

Let $$B(a, b)$$. Since P divides AB in the ratio $$3 : 5$$,

$$-4 = \frac{3 \times a + 5 \times 2}{3 + 5}$$

$$\Rightarrow -32 = 3a + 10$$

$$\Rightarrow 3a = -42$$

$$\Rightarrow a = -14$$

$$1 = \frac{3 \times b + 5 \times (-2)}{3 + 5}$$

$$\Rightarrow 8 = 3b - 10$$

$$\Rightarrow 3b = 18$$

$$\Rightarrow b = 6$$

Hence the co-ordinates of B are $$B(-14, 6)$$.