Question

Find the coordinates of the point which divides the line segment joining (-3,5) and (4, -9) in the ratio 1: 6 internally.

• A. $(-2,-3)$
• B. $(2,3)$
• C. $(-2,3)$
• D. $(2,-3)$

Answer 1

The correct option is C

$(-2,3)$

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:

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

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

$h=\frac{(1\times 4)+(6\times -3)}{7}=\frac{4-18}{7}=\frac{-14}{7}=-2$

$k=\frac{(1\times -9)+(6\times 5)}{7}=\frac{-9+30}{7}=\frac{21}{7}=3$

$\therefore \text{The point is (-2,3)}$