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Question
If the points A(– 3, 9), B(a, b) and C(4, – 5) are collinear and if a + b = 1, then find a and b
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Solution
Since the three points are collinear
Area of a ∆ = 0
`1/2[(x_1y_2 + x_2y_3 + x_3y_1) -(x_2y_1 + x_3y_2 + x_1y_3)]` = 0
`1/2[(-3"b" - 5"a" + 36) - (9"a" + 4"b" + 15)]` = 0
– 3b – 5a + 36 – 9a – 4b – 15 = 0
– 7b – 14a + 21 = 0
– b – 2a + 3 = 0 ...(÷ by 7)
2a + b – 3 = 0
Given 2a + b = 3 ...(1)
a + b = 1 ...(2)
(–) (–) (–)
Subtract (1) and (2) ⇒ a = 2
Substitute the value of a = 2 in (2)
⇒ 2 + b = 1
b = 1 – 2
= – 1
The value of a = 2 and b = – 1
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