Question

An equilateral triangle whose orthocentre is $(3,-2)$ and one side is X-axis, then vertex of triangle which is not on X-axis is

• A. $(3,-6)$
• B. $(1,-2)$
• C. $(9,-2)$
• D. $(3-3)$

Answer 1

The correct option is A $(3,-6)$

$M=(3,0)$

$0\equiv (3,-2)\Rightarrow OM=2$

In equilateral $\Delta \Rightarrow$

$\frac{AO}{OM}=\frac{2}{1}\Rightarrow AO=2\times OM$

$=2\times 2$

$AO=4$

$\therefore AM=AO+OM=4+2=6$

$\therefore A\equiv (3,-6)$