Question

If $P(9a-2,-b)$ divides the line segment joining $A(3a+1,-2)$ and $B(8a,5)$ in the ratio $3:1$. Find the value of $a$ and $b$.

Answer 1

Point $P$ divides $AB$ in the ratio $3:1$

By using section formula

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

$\therefore \frac{3\left(8a\right)+3a+1}{4}=9a-2$

$\Rightarrow 9a=9$

$\Rightarrow a=1$

And,

$\frac{3\left(5\right)+1(-2)}{4}=-b$

$\Rightarrow -4b=13$

$\Rightarrow b=\frac{-13}{4}$