Question

Find the point (x, y) that divides line segment joining the points A(3,6) and B(7,10) in the ratio 3:1.

• A. (8,9)
• B. (4,5)
• C. (6,9)
• D. None of these

Answer 1

The correct option is C

(6,9)

If (x, y) divides the join of $(x_1,y_1)$ 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).