Question

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

• A. $(0,0)$
• B. $(1,0)$
• C. $(0,1)$
• D. $(1,1)$

Answer 1

Answer: (A)

$(0,0)$

Using the section formula, if a point $(x,y)$ divides the line joining the
points $(x_1,y_1)$ and $(x_2,y_2)$ in the
ratio $m:n$ internally, then $(x,y)\equiv (\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Substituting $(x_1,y_1)=(1,-3)$ and $(x_2,y_2)=(-3,9)$ and $m=1,n=3$ in the section formula, we get
the point $(\frac{1(-3)+3\left(1\right)}{1+3},\frac{1\left(9\right)+3(-3)}{1+3})=(0,0)$