Find the point (x,y) that divides the join of A(3,6) and B(7,10) in the ratio 3:1

(8,9).

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(4,5)

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(6,9)

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None of these

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Solution

The correct option is C (6,9)
If (x,y) divides the join of A $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ in the ratio m:n

Then, x = $\frac{m x_{2} + n x_{1}}{m + n}$ and y = $\frac{m y_{2} + n y_{1}}{m + n}$

Here, $x_{1} = 3$ , $x_{2} = 7$ , $y_{1} = 6$ , $y_{2} = 10$ , m = 3 and n = 1.

x = $\frac{3 \times 7 + 1 \times 3}{3 + 1}$ and y = $\frac{3 \times 10 + 1 \times 6}{3 + 1}$

x = 6 and y = 9

Therefore the point is (6,9)

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