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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 .
Solution
It is given that P divides AB in the ratio 3 : 1.
Therefore, by section formula we have
\[\Rightarrow 9a - 2 = \frac{3\left( 8a \right) + 1\left( 3a + 1 \right)}{3 + 1}\]
\[ \Rightarrow 4\left( 9a - 2 \right) = 24a + 3a + 1\]
\[ \Rightarrow 36a - 8 = 27a + 1\]
\[ \Rightarrow 9a = 9\]
\[ \Rightarrow a = 1\]
And ,
\[\Rightarrow - b = \frac{3\left( 5 \right) + 1\left( - 3 \right)}{3 + 1}\]
\[ \Rightarrow - 4b = 15 - 3\]
\[ \Rightarrow b = - 3\]
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