What are coordinates for A', B', C'?

How do i simply this expression (quadratic formula basis) on a ti-84 or normal calculator?

Which coefficient matrix represents a system of linear equations that has a unique solution ? options in photo*

The pyraminx is a rubik's cube-type toy in the shape of a tetrahedron. the pyraminx shown below has edges 15\,\text{cm}15cm long and vertical height h=12.2\,\text{cm}h=12.2cm. the triangle drawn with dashed lines is a right triangle. what is the distance rr? round your answer to the nearest tenth.