Question

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

• A. $\frac{13}{7},\frac{20}{7}$
• B. $\frac{15}{7},\frac{22}{7}$
• C. (2, 3)
• D. (4,3)

Answer 1

The correct option is A $\frac{13}{7},\frac{20}{7}$

Let the coordinates of the point which divides AB in the ratio 3:4 be (x, y).

We know that the coordinates of the point that divides (internally) a line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m : n are

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

By substituting the given values, we get

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

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

$\therefore$ Coordinates of the point which divides (internally) the line segment AB in the ratio 3 : 4 are $(\frac{13}{7},\frac{20}{7})$.