Question

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).

Answer 1

Suppose the point (-1, 6) divides the given line segment in the ratio m₁: m₂ and the coordinates of the ends of the line segment are (-3, 10) and (6, -8).

`x = (m_1x_2 + m_2x_1)/(m_1 + m_2)`

`-1 = (m_1 xx 6 + m_2 xx (-3))/(m_1 + m_2)`

⇒ 6m₁ - 3m₂ = -m₁ - m₂

⇒ 6m₁ + m₁ = 3m₂ - m₂

⇒ 7m₁ = 2m₂

⇒ `"m"_1/"m"_2 = 2/7`

⇒ m₁ : m₂ = 2 : 7

Therefore, the required ratio is 2:7.

Answer 2

Let the ratio in which the line segment joining (-3, 10) and (6, -8) is divided by point (-1, 6) be k : 1.

Therefore, -1 = `(6k-3)/(k+1)`

-k - 1 = 6k -3

7k = 2

k = `2/7`

Therefore, the required ratio is 2:7.