Question

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

• A. (13/7 , 20/7)
• B. (15/7 , 22/7)
• C. (2 , 3)
• D. (4,3)

Answer 1

The correct option is A

(13/7 , 20/7)

The equation for the point that divides a line in the ratio
m:n is,

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

Where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of the line. Substituting in the equation, we get

= ($\frac{3\times 3+4\times 1}{3+4},\frac{3\times 4+4\times 2}{3+4}$)

= ($\frac{13}{7},\frac{20}{7}$)

The point which divides the line segment in the ratio 3:4 is,

($\frac{13}{7},\frac{20}{7}$)