The ratio in which the join of (2, 4) and (10, 12) is divided by the line x = 7 is :

1. 3 : 5

2. 5 : 3

3. 1 : 5

4. 3 : 1

Any point on the line x = 7, can be defined as (7, y).

Let point (7, y) divide line joining (2, 4) and (10, 12) in ratio k : 1.

By section-formula,

(x, y) = $\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big)

Substituting values we get :

$\Rightarrow (7, y) = \Big(\dfrac{k \times 10 + 1 \times 2}{k + 1}, \dfrac{k \times 12 + 1 \times 4}{k + 1}\Big) \\[1em] \Rightarrow (7, y) = \Big(\dfrac{10k + 2}{k + 1}, \dfrac{12k + 4}{k + 1}\Big) \\[1em] \Rightarrow 7 = \dfrac{10k + 2}{k + 1} \\[1em] \Rightarrow 7(k + 1) = 10k + 2 \\[1em] \Rightarrow 7k + 7 = 10k + 2 \\[1em] \Rightarrow 10k - 7k = 7 - 2 \\[1em] \Rightarrow 3k = 5 \\[1em] \Rightarrow k = \dfrac{5}{3}.$

Substituting value of k in k : 1, we get :

⇒ $\dfrac{5}{3} : 1$

⇒ 5 : 3.

Hence, Option 2 is the correct option.