JEE Main 12 Jan 2019 Morning Question 8
Question: If the straight line, $ 2x-3y+17=0 $ is perpendicular to the line passing through the points (7, 17) and $ (15,\beta ), $ then $ \beta $ equals [JEE Main Online Paper Held On 12-Jan-2019 Morning]
Options:
A) 5
B) $ \frac{35}{3} $
C) $ -\frac{35}{3} $
D) $ -5 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ m _1= $ slope of line $ 2x-3y+17=0 $ and $ m _2= $ slope of line joining (7, 17) and $ (15,\beta ) $
$ \therefore $ $ m _1=\frac{2}{3} $ and $ m _2=\frac{\beta -17}{15-7}=\frac{\beta -17}{8} $ Since, both the lines are perpendicular.
$ \therefore $ $ m _1m _2=-1 $
$ \Rightarrow $ $ \frac{2}{3}\times \frac{\beta -17}{8}=-1\Rightarrow \beta -17=-12\Rightarrow \beta =5 $
