Question

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

Answer 1

It is given that P divides AB in the ratio 3 : 1.
Therefore, by section formula we have
$P(9a-2,-b)=(\frac{3\left(8a\right)+1(3a+1)}{3+1},\frac{3\left(5\right)+1(-3)}{3+1})$

$\Rightarrow 9a-2=\frac{3\left(8a\right)+1(3a+1)}{3+1}$ and $\Rightarrow -b=\frac{3\left(5\right)+1(-3)}{3+1})$

$\Rightarrow 9a-2=\frac{27a+1}{4}$ and $\Rightarrow -b=\frac{12}{4}$

$\Rightarrow a=1$ and $b=-3$