Question

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

Answer 1

Let C(-1, 6) divides the line segment AB in the ratio m:n

Here, (x, y) = (-1, 6); (x₁, y₁) = (-3, 10) and (x₂, y₂) = (6, -8)

⇒ -m – n = 6m - 3n and 6m + 6n = -8m + 10n

⇒ -m – 6m – n + 3n = 0 and 6m + 8m + 6n – 10n = 0

⇒ -7m + 2n = 0 and 14m - 4n = 0

⇒ 2n = 7m and 4n = 14m

⇒ 7m = 2n

⇒ m/n = 2/7

Hence, the ratio is 2:7 and the division is internal.