Question

The complex number a + i , -4 + 4i , 4 + 6i are the vertical s A , B, C of the triangle of the argent place . Prove that the triangle is isosceles . If the triangle is be converted into the rhombus then determine the Point D.

Answer 1

It is easy to observe that $AB=AC=\sqrt{34}$

If it is be canverted into a rhombus then BC = $\sqrt{68}$

must be the digonal , hence if D be (x , y ) then digonal bisect .

$\therefore \frac{x+1}{2}=0,\frac{x+1}{2}=5,$

$\therefore (x,y)is(-1,9)orDis-1+9i$