Question

Example 7: In what ratio does the point (-4, 6) divide the line segment joining the
points A(-6, 10) and B(3,-8?
​

Answer 1

Given:-

• A(-6, 10) = x₁, y₁
• B(3, -8) = x₂, y₂
• P(-4, 6) = α, β

To find:-

• m : n

Answer:-

Let the ratio in white AB is divided be m : n.

We have to use the section formula for internal division. It says that,

If P(α, β) divides a line segment AB with A(x₁, y₁) and B(x₂, y₂) internally in the ratio m : n, then,

• α = [(mx₂ + nx₁) / (m + n)]
• β = [(my₂ + ny₁) / (m + n)]

Considering α:-

α = [(mx₂ + nx₁) / (m + n)]

→ -4 = [{(m * 3) + (n * -6)} / (m + n)]

→ -4 = [{3m - 6n}] / (m + n)]

→ -4(m + n) = 3m - 6n

→ -4m - 4n = 3m - 6n

→ 7m = 2n

→ m : n = 2 : 7 Ans.

If we consider β, then also we will get same result.

Considering β:-

β = [(my₂ + ny₁) / (m + n)]

→ 6 = [{(m * -8) + (n * 10)} / (m + n)]

→ 6 = [{-8m + 10n} / (m + n)]

→ 6(m + n) = 10n - 8m

→ 6m + 6n = 10n - 8m

→ 14m = 4n

→ 7m = 2n

→ m : n = 2 : 7 Ans.