Question
If P(9a, -2, -b) divides line segment joining A(3a + 1, -3) and B(8a, 5) in the ratio 3 : 1, find the values of a and b.
✓
Answer
Let P(9a - 2, -b) divides AS internally in the ratio 3 : 1.By section formula,
By section fotmula, the coordinates of point P are given as:
$\Big(\frac{\text{m}_2\text{x}_1+\text{m}_1\text{x}_2}{\text{m}_1+\text{m}_1},\frac{\text{m}_2\text{y}_1+\text{m}_1\text{y}_2}{\text{m}_1+\text{m}_2}\Big)$
$=\Big(\frac{3(8\text{a})+1(3\text{a}+1)}{3+1}.\frac{3(5)+1(-3)}{3+1}\Big)$
$\Rightarrow9\text{a}-2=\frac{3(8\text{a})+1(3\text{a+1})}{3+1}$
and $-\text{b}=\frac{3(5)+1(-3)}{3+1}$
$\Rightarrow9\text{a}-2=\frac{24\text{a}+3\text{a}+1}{4}$
and $-\text{b}=\frac{15-3}{4}$
$\Rightarrow9\text{a}-2=\frac{27\text{a}+1}{4}$
and $-\text{b}=\frac{12}{4}$
$\Rightarrow36\text{a}-8=27\text{a}+1$
and $\text{b}=-3$
Hence proved a = 1 and b = -3.
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