Question

Find the co-ordinates of the point P which divides the line segment AB joining the two points $A(1,-4)$ and $B(4,2)$ externally in the ratio $5:2$

• A. $(6,6)$
• B. $(18,18)$
• C. $(2,2)$
• D. $(5,5)$

Answer 1

The correct option is A $(6,6)$

Using the section formula, if a point
$(x,y)$ divides the line joining the points $(x_1,y_1)$ and
$(x_2,y_2)$externally in the ratio $m:n$, then $(x,y)=(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n{y}_1}{m-n})$
Substituting $(x_1,y_1)=(1,-4)$ and $(x_2,y_2)=(4,2)$ and $m=5,n=2$ in the section formula, we get the point $=(\frac{5\left(4\right)-2\left(1\right)}{5-2},\frac{5\left(2\right)-2(-4)}{5-2})=(6,6)$