Question

If the points A (-3,9) , B (a,b) , C (4,-5) are collinear and a + b = 1 , then find the values of a and b.​

Answer 1

Step-by-step explanation:

Since its colllinear... So the diterminate value should be zero.... Comment the answer

Answer 2

The value of a=2 and b=-1.

Step-by-step explanation:

Given : If the points A (-3,9) , B (a,b) , C (4,-5) are collinear  and a + b = 1.

To find : The values of a and b. ?

Solution :

If the points A (-3,9) , B (a,b) , C (4,-5) are collinear then the slope of AB = slope of BC.

Slope of two point is $m=\frac{y_2-y_1}{x_2-x_1}$

Slope of AB = $\frac{b-9}{a-(-3)}=\frac{b-9}{a+3}$

Slope of BC = $\frac{-5-b}{4-a}$

Equate the slopes,

$\frac{b-9}{a+3}=\frac{-5-b}{4-a}$

Cross multiply,

$(b-9)(4-a)=(-5-b)(a+3)$

Substitute a=1-b,

$(b-9)(4-(1-b))=(-5-b)((1-b)+3)$

$(b-9)(3+b)=(-5-b)(4-b)$

$3b+b^2-27-9b=-20+5b-4b+b^2$

$-7b=7$

$b=-1$

Substitute in a=1-b,

$a=1-(-1)=2$

Therefore, the value of a=2 and b=-1.

#Learn more

Show that the point are collinear (-3,-7),(4,7) and (5,9),

https://brainly.in/question/3551457