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 value of a.
a = ___.

Answer 1

Applying section formula, we have

For $x$ coordinate,

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

$9a-2=\frac{24a+3a+1}{(3+1)}$
$4(9a-2)=27a+1$
$36a-8=27a+1$
$9a=9$
$a=1$.

For $y$ coordinate,
$-b=\frac{(3\times 5)+(1\times (-3\left)\right)}{(3+1)}$
$-4b=15-3$
$-4b=12$, so $b=-3$.