JEE Mains · Maths · STD 11 - Trigonometrical equations
If a \(\triangle ABC\) has vertices \(A (-1,7), B (-7,1)\) and \(C (5,-5),\) then its orthocentre has coordinates
- A \((3,-3)\)
- B \(\left(-\frac{3}{5}, \frac{3}{5}\right)\)
- C \((-3,3)\)
- D \(\left(\frac{3}{5},-\frac{3}{5}\right)\)
Answer & Solution
Correct Answer
(C) \((-3,3)\)
Step-by-step Solution
Detailed explanation
Let orthocentre is \(H \left( x _{0}, y _{0}\right)\) \(m _{ AH } \cdot m _{ BC }=-1\) \(\Rightarrow \quad\left(\frac{ y _{0}-7}{ x _{0}+1}\right)\left(\frac{1+5}{-7-5}\right)=-1\) \(\Rightarrow \quad 2 x _{0}- y _{0}+9=0 \quad \ldots \ldots\) and…
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