Question

If Point P (-4,6) divides the line segment AB with A(-6,10) and B(x,y) in the ratio 3:2 internally, find the co-ordinates of B.

• A. $(\frac{11}{3},\frac{14}{3})$
• B. $(\frac{8}{3},\frac{-10}{3})$
• C. $(\frac{-8}{3},\frac{10}{3})$
• D. $(\frac{-16}{3},\frac{8}{3})$

Answer 1

The correct option is C $(\frac{-8}{3},\frac{10}{3})$

The equation for the point that divides a line segment joining the points $(x_1,y_1)\text{and}(x_2,y_2)$ in the ratio m : n is: $(\frac{(n\times x_1+m\times x_2)}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

Here,
$(x_1,y_1)=(-6,10),(x_2,y_2)=(x,y),m:n=3:2$
According to Section Formula:
$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
$\Rightarrow (-4,6)=(\frac{3x+(-12)}{3+2},\frac{3y+20}{3+2})$
$\Rightarrow -4=\frac{3x-12}{5}\text{and}6=\frac{3y+20}{5}$
$\Rightarrow 3x=-20+12\text{and}3y=30-20$
$\Rightarrow x=\frac{-8}{3}\text{and}y=\frac{10}{3}$
$\therefore$ Co-ordinates of B are $(\frac{-8}{3},\frac{10}{3})$.