Question

if the points (x+1,2),(1,x+2),(1/x+1,2/x+1) are collinear then x is​

Answer 1

Answer:

x = 0 or -4.      

Step-by-step explanation:

Given points are A (x+1, 2),  B (1 , x+2), and C ( 1/(x+1),  2/(x+1)  ).

A, B and C are collinear meaning that they lie on the same straight line.

Let the straight line be :   a x + b y = c

Slope of AB = slope of  AC = m

So    (x+2 - 2) / (1 - x - 1) = [2/(x+1) - x-2] / [1/(x+1) - 1] = m  

=>   -1 = m

 =>     [ 2 - (x+1)(x+2) ] /(x+1)  =  - [ 1 - x - 1]/(x+1)

 =>       x² + 3 x = - x

 =>       x = 0 or  x = - 4.

A, B and C are  (1,2), (1, 2), (1, 2)

or   (-3,2),  (1, -2), and (-1/3, -2/3).

Answer 2

Answer:

Step-by-step explanation:

Let A(x,-1)

B(2,1)

C(4,5)

If ABC is collinear then ar(ABC)=0

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

1/2[x(1-5)+2(5+1)+4(-1-1)]=0

x(-4)+2(6)+4(-2)=0

-4x+12-8=0

-4x+4=0

4=4x

x=1