Calculate the ratio in which the line segment A(6, 5) and B(4, -3) is divided by the line y = 2.

We know that, y-coordinate on any point of the line y = 2 is 2. Let coordinate be x.

Point = (x, 2)

Let ratio in which point divides line segment AB is k : 1.

By section-formula,

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

Substituting values for y-coordinate we get,

$\Rightarrow 2 = \dfrac{k \times (-3) + 1 \times 5}{k + 1} \\[1em] \Rightarrow 2(k + 1) = -3k + 5 \\[1em] \Rightarrow 2k + 2 = -3k + 5 \\[1em] \Rightarrow 2k + 3k = 5 - 2 \\[1em] \Rightarrow 5k = 3 \\[1em] \Rightarrow k = \dfrac{3}{5}.$

k : 1 = $\dfrac{3}{5} : 1$ = 3 : 5.

Hence, ratio in which the line segment A(6, 5) and B(4, -3) is divided by the line y = 2 is 3 : 5.