Question

$(-4,3)$ and $(4,3)$ are vertices of equilateral triangle. Find the third vertex?

• A. $(10,4\sqrt{3}+3)$
• B. $(0,-4\sqrt{3}+3)$
• C. $(0,4\sqrt{3}+3)$
• D. None of these

Answer 1

The correct option is C $(0,4\sqrt{3}+3)$

$(-4,3)(4,3)$ are equivalent triangle vertices

$AB=BC=CA=\sqrt{(4+4{)}^2+(3-3{)}^2}=8.$

$\sqrt{(x+9{)}^2+(y-3{)}^2}=8$........(i)

$\sqrt{(x-9{)}^2+(y-3{)}^2}=8$......(ii)

from$\left(i\right)$ and $\left(ii\right)$

$x=o,y=4\sqrt{3}+3.$

$A(0,4\sqrt{3}+3)$