Question

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

Answer 1

Answer:

b=47/3and-44/3 apply triangle. law and put equal to 0

Answer 2

a = $\dfrac{1}{12}$ and b =$\dfrac{11}{12}$

Step-by-step explanation:

The given three points P(- 3, 9), Q(a, b) and R(4, 5) are collinear.

To find, the values of  a and b=

We know that,

The condition of three points are collinear.

$x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})=0$

⇒ $(-3)(b-5)+a(5-9)+4(9-b)=0$

⇒ - 3b + 15 + 5a - 45 + 36 - 45 = 0

⇒ 5a - 7b = - 6         ....... (1)

And given by question,

a + b = 1                   ....... (2)

Multiplying (2) by 7 and adding them, we get

5a - 7b + 7a + 7b = - 6 + 7

⇒ 12a = 1

⇒ a = $\dfrac{1}{12}$

Putting the value of a in (2), we get

$\dfrac{1}{12}$ + b = 1    

⇒ b = 1 - $\dfrac{1}{12}$ =$\dfrac{11}{12}$

∴ a = $\dfrac{1}{12}$ and b =$\dfrac{11}{12}$