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If (x, y) divides the line segment joining (6, 5) and (4, 7) in the ratio 1 : 1 internally, then find the value of (x, y).
1. (3, 4)
2. (4, 3)
3. (5, 6)
4. (8, 5)

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Correct Answer - Option 3 : (5, 6)

Given:

(x, y) divides the line segment joining (6, 5) and (4, 7) 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 × 4 + 1 × 6)/(1 + 1)

⇒ x = (4 + 6)/2

⇒ x = 10/2

⇒ x = 5

y = (my2 + ny1)/(m + n)

⇒ y = (1 × 7 + 1 × 5)/(1 + 1)

⇒ y = (7 + 5)/2

⇒ y = 12/2

⇒ y = 6

∴ The value of (x, y) is (5, 6).

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