Question

If (x, y) divides the line segment joining (4, 3) and (2, 5) in the ratio 1 : 1 internally, then find the value of (x, y).
1. (3, 4)
2. (4, 3)
3. (5, 8)
4. (8, 5)

Answer 1

Correct Answer - Option 1 : (3, 4)

Given:

(x, y) divides the line segment joining (4, 3) and (2, 5) in the ratio 1 : 1 internally.

Formula Used:

x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Calculation:

x = (mx₂ + nx₁)/(m + n)

⇒ x = (1 × 2 + 1 × 4)/(1 + 1)

⇒ x = (2 + 4)/2

⇒ x = 6/2

⇒ x = 3

y = (my₂ + ny₁)/(m + n)

⇒ y = (1 × 5 + 1 × 3)/(1 + 1)

⇒ y = (5 + 3)/2

⇒ y = 8/2

⇒ y = 4

∴ The value of (x, y) is (3, 4).