Question

Find the point which divides the line segment joining the points (2, -6) and (3, 6) in the ratio 2 : 3.

• A. $(\frac{12}{5},-\frac{6}{5})$
• B. $(\frac{12}{5},\frac{6}{5})$
• C. $(-\frac{12}{5},-\frac{6}{5})$
• D. $(-\frac{12}{5},\frac{6}{5})$

Answer 1

The correct option is A

$(\frac{12}{5},-\frac{6}{5})$

If a point $P(x,y)$ divides a line segment joining $(x_1,y_1)and(x_2,y_2)$ in the ration $m:n$, then the coordinates of P are given by:

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

$\text{Let the coordinates of the point be (h,k)}$

$h=\frac{(2\times 3)+(3\times 2)}{2+3}=\frac{6+6}{5}=\frac{12}{5}$

$k=\frac{(2\times 6)+(3\times -6)}{2+3}=\frac{12-18}{5}=-\frac{6}{5}$

$\therefore$ The required point is $(\frac{12}{5},-\frac{6}{5})$