| If the points \[(x+1,2),\]\[(1,x+2),\]\[\left( \frac{1}{x+1},\frac{2}{x+1} \right)\] are collinear, then x is |
A) \[4\]
B) 5
C) \[-\,\,4\]
D) None of these
Correct Answer: C
Solution :
| Since, the points are collinear. |
| Hence, there slopes are equal. |
| Now, \[\frac{(x+2)-2}{1-(x+1)}=\frac{\left( \frac{2}{x+1} \right)-(x+2)}{\left( \frac{1}{x+1} \right)-1}\] |
| \[\Rightarrow \] \[-\,\,1=\frac{2-({{x}^{2}}+3x+2)}{1-(x+1)}\] |
| \[\Rightarrow \] \[x=-\,\,4\] |
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