Q28 of 31 Page 1

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 & b.

Given: Point P(9a – 2, –b) divides the line segment joining A(3a + 1, –3) and B(8a, 5) in ratio 3:1


Section formula


If a point P(x, y) divides a line segment joining A(x1, y1) and B(x2, y2) in a ratio m:n, then coordinates of P are



Putting values, we get




On comparison,



⇒ 36a – 8 = 27a + 1


⇒ 9a = 9


⇒ a = 1


And


–b = 3


⇒ b = –3


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