If the point P(6, 2) divides the line segment joining A(6, 5) and B(4, y) in the ratio 3 : 1, then the value of y is :

1. 1

2. 2

3. 3

4. 4

Let point P be (6, 2).

Given,

m₁ : m₂ = 3 : 1

P(6, 2) divides the line segment joining A(6, 5) and B(4, y) in the ratio 3 : 1.

By section-formula,

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

We use the y–coordinate to find y.

$\Rightarrow 2 = \dfrac{3 \times y + 1 \times 5}{3 + 1} \\[1em] \Rightarrow 2 = \dfrac{3y + 5}{4} \\[1em] \Rightarrow 8 = 3y + 5 \\[1em] \Rightarrow 3y = 3 \\[1em] \Rightarrow y = 1.$

Hence, Option 1 is the correct option.