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✤ Required Answer:
✒ GiveN:
✒ To FinD:
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✤ How to Solve?
Basically, Collinear points refer to the points that lie on the same straight line. Sum of distance between any two points of two pairs is equal to length of distance between the third pair.
By using formula for area,
➤ Area of triangle = 0
✒ So, By using this condition for three collinear points, let's solve this question....
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✤ Solution:
Let,
By applying the above condition,
Given in the question,
Subtracting eq(2) from eq(1),
Putting value of a in eq(2),
❇ Hence, Required values of a and b
✒ Hence, solved !!
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Verified answer
Step-by-step explanation:
As per the given questions
Let P (x₁ = −3, y₁ = 9), Q(x₂ = a, y₂ = b) and R(x₃ = 4, y₃ = −5) be the given points.
The given points are collinear if
x₁ (y₂ − y₃) + x₂ (y₃ − y₁) + x₃ (y₁ − y₂) = 0
Now put the given values, we get
-3 (b + 5) + a (−5 − 9) + 4 (9 − b) = 0
⇒ −3b − 15 − 14a + 36 − 4b = 0
⇒ 2a + b = 3 ......................equation (i)
And a + b = 1 (given) ..........equation (ii)
Now, on subtracting (i) - (ii), we get
a = 2
Substitute this value in equation (ii), we get
2 + b = 1
b = -1
Hence, a = 2 and b = −1.
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