Question

Find the point (x,y) that divides the line joining 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 $A(x_1,y_1)and(x_2,y_2)$ in the ratio m:n

Then, $x=\frac{m{x}_2+n{x}_1}{m+n}andy=\frac{m{y}_2+n{y}_1}{m+n}$

Here, $x_1=3,x_2=7,y_1=6,y_2=10$, m = 3 and n = 1.

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

x = 6 and y = 9

Therefore the point is (6, 9).