Question

The point that divides the line segment joining A (3, 6) and B (7, 10) in the ratio 3 : 1 is .

• A. (4 , 5)
• B. (8 , 9)
• C. (6 , 9)

Answer 1

The correct option is C (6 , 9)

If a point (x,y) divides the line segment joining the points A$(x_1,y_1)$ and B$(x_2,y_2)$ in the ratio m : n,

then, x = $\left(\frac{m{x}_2+n{x}_1}{m+n}\right)$ and y = $\left(\frac{m{y}_2+n{y}_1}{m+n}\right)$

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

x = $\frac{3\left(7\right)+1\left(3\right)}{3+1}$ and y = $\frac{3\left(10\right)+1\left(6\right)}{3+1}$

x = 6 and y = 9

$\therefore$ The point is (6,9).