Question

Find the coordinates of the point $X$ that divides the join of $A(7,4)$ and $B(-3,6)$ in the ratio $1:3$

• A. $(\frac{9}{2},\frac{11}{2})$
• B. $(\frac{9}{2},\frac{5}{2})$
• C. $(\frac{9}{2},\frac{9}{2})$
• D. $(\frac{2}{9},\frac{2}{9})$

Answer 1

The correct option is C $(\frac{9}{2},\frac{9}{2})$

Given the two points $A(7,4)$ and $B(-3,6)$ and ratio $m:n=1:3$

Here we apply the section formula : 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

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

$\therefore$ By section formula

$(x,y)=(\frac{1\times (-3)+3\times 7}{1+3},\frac{1\times 6+3\times 4}{1+3})=(\frac{-3+21}{4},\frac{6+12}{4})=(\frac{18}{4},\frac{18}{4})=(\frac{9}{2},\frac{9}{2})$