If the point P(k, 0) divides the line segment joining the points A(2, -2) and B(-7, 4) in the ratio 1 : 2, then the value of k is:

1. -2

2. -1

3. 1

4. 2

Given,

P = (k, 0)

m₁ : m₂ = 1 : 2

P(k, 0) divides the line segment joining the points A(2, -2) and B(-7, 4) in the ratio 1 : 2.

By section-formula,

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

Substituting values we get :

$\Rightarrow (k, 0) = \Big(\dfrac{1 \times (-7) + 2 \times 2}{1 + 2}, \dfrac{1 \times 4 + 2 \times (-2)}{1 + 2}\Big) \\[1em] \Rightarrow (k, 0) = \Big(\dfrac{-7 + 4}{3}, \dfrac{4 - 4}{3}\Big) \\[1em] \Rightarrow (k, 0) = \Big(\dfrac{-3}{3}, \dfrac{0}{3}\Big) \\[1em] \Rightarrow (k, 0) = (-1, 0).$

Thus, k = -1.

Hence, Option 2 is the correct option.