Question

Find the value of a and b if the points A (-2,1 ) ,B ( a,b ) , C (4,-1 ) are Collinear and a-b = 1.

Answer 1

Hey!

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Given that the given points are collinear
The ar ∆ABC = 0


1/2 [ x1 (y2 - y1) + x2 (y3 - y1) + x3 (y1 - y2) ] = 0

Given,
x1 = -2 , y1 = 1
x2 = a , y2 = b
x3 = 4 , y3 = -1

Putting the values,

1/2 [ -2 (b + 1) + a ( -1 -1) + 4 ( 1 - b)] = 0

-2b - 2 - 2a + 4 - 4b = 0

2a + 6b = 2

a + 3b = 1 _________________ (i)

Given,
a - b = 1 _________________ (ii)

Subtracting (i) from (ii)

-4b = 0
b = 0

Substituting the value of 'b' in (ii)
a - 0 = 1
a = 1


Thus,
a = 1
b = 0

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Hope it helps ...!!!

Answer 2

with the help of area of triangle we can find value of a and b.