Question

if the points P(-3,9),Q(a,b) and R(4,-5) are collinear and a+b=1,find the values of a and b.

Answer 1

Please look the attachment below.

Answer 2

Answer:

a = 2 and b = −1.

Step-by-step explanation:

As per the given questions

Let  A (x₁ = −3, y₁ = 9), B(x₂ = a, y₂ = b) and C(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.