The line x + y = 4 bisects the line segment joining the points (0, k) and (4, 0), the value of k is :

1. 2

2. 4

3. -4

4. -2

Given,

Points : (0, k) and (4, 0)

By formula,

Mid-point : $\Big(\dfrac{x$1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get :

$\text{Mid-point } = \Big(\dfrac{0 + 4}{2}, \dfrac{k + 0}{2}\Big) \\[1em] = \Big(\dfrac{4}{2}, \dfrac{k}{2}\Big) \\[1em] = \Big(2, \dfrac{k}{2}\Big).$

Given,

Line x + y = 4 bisects the line segment joining the points (0, k) and (4, 0).

∴ Line x + y = 4 passes through the point $\Big(2, \dfrac{k}{2}\Big)$.

Substituting value we get :

$\Rightarrow 2 + \dfrac{k}{2} = 4 \\[1em] \Rightarrow \dfrac{k}{2} = 4 - 2 \\[1em] \Rightarrow \dfrac{k}{2} = 2 \\[1em] \Rightarrow k = 4.$

Hence, Option 2 is the correct option.