Question

Line segment joining points (4, 3) and (1, −2) is divided by the point (y, 0) in the ratio ______.

Options

• 2 : 3

• 3 : 2

• 3 : 4

• 4 : 2

Answer 1

Line segment joining points (4, 3) and (1, −2) is divided by the point (y, 0) in the ratio 3 : 2.

Explanation:

Let (y, 0) divide the line segment joining the points (4, 3) and (1, -2) in the ratio k : 1.

By section-formula,

(x, y) = `((m_1x_2 + m_2x_1)/(m_1 + m_2), (m_1y_2 + m_2y_1)/(m_1 + m_2))`

Substituting values for y-coordinate:

⇒ 0 = `(k × −2 + 1 × 3​)/(k + 1)`

⇒ −2k + 3 = 0 

⇒ 2k = 3

⇒ k = `3/2`

Substituting value of k in k : 1, we get:

⇒ `3/2 : 1`

⇒ 3 : 2