Question

A(2, 4) and B(8, 12) are two ends of a line segment. Find the point which divides AB internally in the ratio 1:3.

• A. (3.75, 5)
• B. (3, 6.5)
• C. (3.5, 6)
• D. (3, 6)

Answer 1

The correct option is C (3.5, 6)

Let the point $P(x,y)$ divide AB in the ratio 1:3.

The coordinates of the point that divides a line segment internally , joining the points $(x_1,y_1)\text{and}(x_2,y_2)$ in the ratio m : n are:

$(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

Here,
$x_1=2,y_1=4x_2=8,y_2=12m=1,n=3$

So, $(x,y)=(\frac{1\times 8+3\times 2}{1+3},\frac{1\times 12+3\times 4}{1+3})$
$=(\frac{14}{4},\frac{24}{4})=(\frac{7}{2},6)$

$\therefore$ The point that divides AB in the ratio 1:3 is $(\frac{7}{2},6)$.