Question

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

Options

• 2

• 4

• −4

• −2

Answer 1

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

Explanation:

Given,

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

By formula,

Mid-point: `((x_1+x_2)/2, (y_1+y_2)/2)`

Substituting values we get:

Mid-point = `((0 + 4)/2, (k + 0)/2)`

= `(4/2, k/2)`

= `(2, k/2)`

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 `(2, k/2)`

Substituting value we get:

⇒ `2 + 2/k​ = 4`

⇒ `2/k​ = 4 − 2`

⇒ `2/k​ = 2`

⇒ k = 4