Hi;
The coordinates of the vertices of an isosceles triangle are integers. Show that the square of the length of its base is an even number.
Any hint would be helphul. Thanks in advance.
Hello,
Let be the coordinates of the summit :
Let and be the coordinates of the two other points :
We know that . Hence
So this can be written :
Now you want to prove that is even.
Now write and
and expand the two squares following this model :
Then simplify and conclude