Question

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

• A. $(2,1)$
• B. $(0,0)$
• C. $(\frac{5}{3},2)$
• D. $(1,-2)$

Answer 1

Answer: (B)

$(0,0)$

Given the two points $A(1,-3)$ and $B(-3,9)$ and ratio $m:n=1:3.$

Here we apply the section formula, i. e. if a point $X(x,y)$ divides the line segment $AB$ joining the points $A(x_1,y_1)\&B(x_2,y_2)$ in the ratio $m:n$ then we have

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

$\therefore$ $(x,y)=(\frac{3\times 1+1\times (-3)}{1+3},\frac{3\times (-3)+1\times 9}{1+3})=(0,0)$