| If the inclination of a line joining the points \[A\,\,(x,-\,\,3)\]and \[B\,\,(2,5)\]is \[135{}^\circ ,\]then \[x\] is equal to |
A) 10
B) 15
C) 20
D) 25
E) None of these
Correct Answer: A
Solution :
| Slope of \[AB=\frac{5+3}{2-x}=\frac{8}{2-x}=\tan 135{}^\circ \] |
| \[\tan \,\,(180{}^\circ -135{}^\circ )=\frac{8}{2-x}\] |
| \[\Rightarrow \]\[-\tan 45{}^\circ =\frac{8}{2-x}\]\[\Rightarrow \]\[-1=\frac{8}{2-x}\] |
| \[\Rightarrow \]\[-\,\,2+x=8\]\[\Rightarrow \]\[x=10\] |
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