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.

• A. a = 1, b = -3
• B. a = -3, b = -1
• C. a = -1, b = 2
• D. a = 3, b = -3

Answer 1

The correct option is A a = 1, b = -3

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,
$-b=\frac{(3\times 5)+(1\times -3)}{(3+1)}$
$-4b=15-3$
$-4b=12$
$b=-3$