The line y = 4 divides the join of points (6, 7) and (4, -1) in the ratio :

1. 3 : 5

2. 5 : 3

3. 1 : 5

4. 5 : 1

Any point on the line y = 4, can be defined as (x, 4).

Let point (x, 4) divide line joining (6, 7) and (4, -1) 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 :

$\Rightarrow (x, 4) = \Big(\dfrac{k \times 4 + 1 \times 6}{k + 1}, \dfrac{k \times -1 + 1 \times 7}{k + 1}\Big) \\[1em] \Rightarrow (x, 4) = \Big(\dfrac{4k + 6}{k + 1}, \dfrac{-k + 7}{k + 1}\Big) \\[1em] \Rightarrow 4 = \dfrac{-k + 7}{k + 1} \\[1em] \Rightarrow 4(k + 1) = -k + 7 \\[1em] \Rightarrow 4k + 4 = -k + 7 \\[1em] \Rightarrow 4k + k = 7 - 4 \\[1em] \Rightarrow 5k = 3 \\[1em] \Rightarrow k = \dfrac{3}{5}.$

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

⇒ $\dfrac{3}{5} : 1$

⇒ 3 : 5.

Hence, Option 1 is the correct option.