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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 and b.

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by shirin2

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by shirin2

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P(x) = m₁x₂ + m₂x₁ / m₁+m₂

⇒ 9a-2 = 3(8a) + 1(3a+1)

⇒ 4(9a-2) = 24a +3a+1

⇒ 36a-8 = 27a +1

⇒ 9a = 9

⇒ a=1

∴ The value of a is 1

P(y) = m₁y₂ + m₂y₁ / m₁+m₂

⇒ -b = 3(5) + 1(-3) / 3+1

⇒ -b = 15 -3 /4

⇒ -b = 12/4

⇒ -b = 3

⇒ b = -3

∴The value of b = -3

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