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  • If P(9a – 2, –b) divides line segment joining A(3a + 1, –3) and B(8a, 5)in the ratio 3 ratio1, find the values of a and b.

 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.

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Solution
              
Point P(9a – 2, –b) divides line segment joining the points A(3a + 1, –3) and B(8a, 5) in ration 3 : 1.
(x1, y1) = (3a+1, -3)                 (x2, y2) = (8a, 5)
m1 = 3, m2 = 1
Using section formula we have
\left ( 9a-2,-b \right )= \left [ \frac{3\left ( 8a \right )+1\left ( 3a+1 \right )}{3+1} ,\frac{3\left ( 5 \right )+1\left ( -3 \right )}{3+1}\right ]
\left ( 9a-2,-b \right )= \left [ \frac{24a+3a+1}{4},\frac{15-3}{4}\right ]
\left ( 9a-2,-b \right )= \left [ \frac{27a+1}{4},\frac{12}{4}\right ]
Equate left-hand side and the right-hand side we get
9a-2= \frac{27a+1}{4}              -b= \frac{12}{4}

36a – 8 = 27a + 1        –b = 3
9a = 9                     b = –3
a= \frac{9}{9}
a = 1

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