Category:Examples of Use of Condition for Points in Complex Plane to form Isosceles Triangle

This category contains examples of use of Condition for Points in Complex Plane to form Isosceles Triangle.

Let $A = z_1 = x_1 + i y_1$, $B = z_2 = x_2 + i y_2$ and $C = z_3 = x_3 + i y_3$ represent on the complex plane the vertices of a triangle.

Then $\triangle ABC$ is isosceles, where $A$ is the apex, if and only if:

${x_2}^2 + {y_2}^2 - 2 \paren {x_1 x_2 + y_1 y_2} = {x_3}^2 + {y_3}^2 - 2 \paren {x_1 x_3 + y_1 y_3}$