Question

If a point P divides the line segment joining $A(5,3)$ and $B(10,8)$ in the ratio $3:2$ internally, then point P lies on:

[1 mark]

• A. $x+y=0$
• B. $x-y+2=0$
• C. $x-y=0$
• D. $x-y-2=0$

Answer 1

The correct option is D $x-y-2=0$


Using the section formula,
$m:n=3:2$
$x_1=5,y_1=3,x_2=10,y_2=8p(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})=(\frac{3\left(10\right)+2\left(5\right)}{5},\frac{3\left(8\right)+2\left(3\right)}{5})$
$P(x,y)=(8,6)$

By substituting the coordinates of P in the given options, we can notice that $P(8,6)$ satisfies the equation $x-y-2=0$
$\therefore P(8,6)$ lies on the line $x-y-2=0$