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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.

1
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9a-2 =3*8a +1* 3a+1

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3 + 1

9a-2 = 24a + 3a + 1

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4

36a - 8 = 27a + 1

36a - 27a= 1 + 8

9a = 9

a = 9

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9

Now,

-b = 3*5 + 1 * -3

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4

-b = 15 - 3

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4

-b = 12/4

-b = 3