You move right 8 units. You end at (5, -4). Where did you start?

She first uses a straight edge to draw a diameter of the circle through the center.

Then, using a compass and straight edge, she constructs the perpendicular bisector of the diameter forming another diameter.

(These resulting four points on the circle are the vertices of the inscribed square.), hence, these points are joined in the next step using a straightedge.