Question

Find the ratio in which the point P(x, 2) divides the join of A(12, 5) and B(4, −3). [CBSE 2014]

Answer 1

Let k be the ratio in which the point P(x, 2) divides the line joining the points A(x₁ = 12, y₁ = 5) and B(x₂ = 4, y₂ = −3). Then
$x=\frac{k\times 4+12}{k+1}\mathrm{and}2=\frac{k\times \left(-3\right)+5}{k+1}$
Now
$2=\frac{k\times \left(-3\right)+5}{k+1}\Rightarrow 2k+2=-3k+5\Rightarrow k=\frac{3}{5}$
Hence, the required ratio is 3 : 5.