Question

the point (8,4)divides the line joining (5,2)and (9,6)in ratio​

Answer 1

Answer:

☢Answer is in the picture..⬆️⬆️

☣Hope it helps....❤❤

Answer 2

Correct question:-

The point (8, 4)divides the line joining (5, -2)and (9, 6) in ratio?

Given:-

• A(5, -2) = x₁, y₁
• B(9, 6) = x₂, y₂
• P(8, 4) = α, β

To find:-

• m : n

Answer:-

Let the ratio in which 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)]

→ 8 = [{(m * 9) + (n * 5)} / (m + n)]

→ 8 = [{9m + 5n} / (m + n)]

→ 8(m + n) = 9m + 5n

→ 8m + 8n = 9m + 5n

→ 9m - 8m = 8n - 5n

→ m = 3n

→ m : n = 3 : 1 Ans.

If we consider β then also we will get same ratio.

Considering β

β = [(my₂ + ny₁) / (m + n)]

→ 4 = [{(m * 6) + (n * -2)} / (m + n)]

→ 4 = [{6m - 2n} / (m + n)]

→ 4(m + n) = 6m - 2n

→ 4m + 4n = 6m - 2n

→ 6m - 4m = 4n + 2n

→ 2m = 6n

→ m = 3n

→ m : n = 3 : 1 Ans.