Question

How to know if points are vertices of isosceles triangle?

Answer 1

I think you want to ask -----> How to identify any triangle is an isosceles triangle if their points are given , right ?

it is simple ! as you know isosceles triangle is a triangle in which length of two sides equal.
so, first of all find length of sides using co-ordinate geometry.
from distance formula, you can get the length of side of triangle.
e.g., if two points $(x_1,y_1)$ and $(x_2,y_2)$ are given then, distance between them = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

now after finding length of side , check which side is equal to other side.
if two sides are equal then, it must be isosceles otherwise not.