Question: If the inclination of a line joining the points $ A(x,-3) $ and $ B(2,5) $ is $ 135{}^\circ , $ then $ x $ is equal to
Options:
A) 10
B) 15
C) 20
D) 25
E) None of these
Show Answer
Answer:
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 $