JEE Main Solved Paper 2017 Question 1
Question: Let k be an integer such that triangle with vertices $ (k,-3k),(5,k) $ and (-k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point: JEE Main Solved Paper-2017
Options:
A) $ ( 2,\frac{1}{2} ) $
B) $ ( 2,-\frac{1}{2} ) $
C) $ ( 1,\frac{3}{4} ) $
D) $ ( 1,-\frac{3}{4} ) $
Show Answer
Answer:
Correct Answer: A
Solution:
- We have $ \frac{1}{2}\ \begin{vmatrix} k & -3k & 1 \\ 5 & k & 1 \\ -k & 2 & 1 \\ \end{vmatrix} =28 $
$ \Rightarrow $ $ 5k^{2}+13k-46=0 $ or $ 5k^{2}+13k+66=0 $ (no real solution exist)
$ \therefore $ $ k=\frac{-23}{5} $ or $ k=2 $ As k is an integer, so k = 2
$ \Rightarrow $ orthocentre is $ ( 2,\frac{1}{2} ) $
