Trapezoid TEAM has the following vertices T(-2,3),

E(1,0), A(7,6) and M(0,5). Points E, F(h,k) and A are on the same line. If T, E, F and M are the vertices of a square, find h and k.

MY WORK:

Since points E, F and A lie on the same line, this tells me that they have the same slope, which I found to be 1.

This is where I got stuck.

Where do I go from there?

I love this coordinate geometry stuff.

I realized that point F lies perfectly somewhere on line segment EA to form a square with the other two vertices given. Is this correct?