Question

If points(-1,3), (4-2) and (a,b) are collinear, then which are of the following relation is true

Answer 1

Step-by-step explanation:

Given: If points(-1,3), (4,-2) and (a,b) are collinear, then

To find: Which of the following relation is true

i) a=b

ii) a+b=2

iii) a=2+b

iv) a=-b

Solution:

Tip: Area of triangle is equal to zero.

If three vertices (x1,y1), (x2,y2), (x3,y3) are given than area of triangle is

$\bold{\red{Area \: of \: triangle = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|}}$

If three points are collinear than area of triangle must equal to zero.

Here points are

(-1,3), (4,-2), (a,b)

$\frac{1}{2} |( - 1)( - 2 - b) + 4(b -3) + a(3 + 2)| = 0$

or

$|( 2 + b) + 4(b -3) + 5a| = 0$

or

$|2 + b + 4b - 12 + 5a| = 0$

or

$5a + 5b = 10 \\ \\ a + b = 2$

Thus, option (ii) is correct.

Final answer:

If points(-1,3), (4,-2) and (a,b) are collinear, then a+b=2.

Thus, option (ii) is correct.

Hope it helps you.

Remark*: Options are added.

To learn more on brainly:

1) If the three points (5,1),(1,-1)and(p,4)are collinear,find the value of p

https://brainly.in/question/40543271

2) If the points A (3, 0, p), B (- I , q, 3) and C(-3. 3. 0) are collinear, then find the values of p and q.

https://brainly.in/question/6649093

Answer 2

Given :  points(-1,3), (4-2) and (a,b) are collinear,

To Find : relation between a and b

Solution:

if  A , B and C are 3 collinear  points then

slope of AB = Slope of BC = Slope of AC

(-1,3), (4-2) and (a,b)

Slope between  (-1,3), (4-2)  

= ( -2 - 3) / ( 4 - (-1)) = - 5 / 5  = - 1

Slope between  (4-2) and (a,b)

=  (b + 2)/ ( a - 4)  = - 1

=> b + 2 = - a  + 4

=> a + b = 2

Hence a + b = 2

Learn More:

A,B and P are the three non-collinear points on a plane. The ...

brainly.in/question/13197890

let P be an interior point of a triangle ABC . let Q and R be the ...

brainly.in/question/9424932