Question

Find the ratio in which the point P(x, 2) divides the join of A(12, 5) and B(4, – 3).

Answer 1

Let the point P(x, 2) divides the join of points A(12, 5) and B(4, –3) in the ratio k : 1.

Therefore, the coordinate of P is given by \((\frac{4k + 12}{k+1}, \frac{-3k+5}{k+1})\)

But given that the co- ordinates of P is (x,2)

∴ (x, 2) = \((\frac{4k + 12}{k+1}, \frac{-3k+5}{k+1})\)

\(\frac{4k + 12}{k+1}, =2 \) & \( \frac{-3k+5}{k+1} = x\) (By comparing corresponding x & y coordinates)

⇒ –3k + 5 = 2k + 2 ⇒ 5k = 5 – 2 = 3 ⇒ k = \(\frac{3}{5}\) .

Now, \(\frac{K}{1} = \frac{\frac{3}{5}}{1} = \frac{3}{5}\) ⇒ k : 1 = 3 : 5. 

Hence, point P divides the join of A(12,5) & B(4,–3) in the ratio 3 : 5.