G.GPE.B.4 and G.GPE.B.5 - Prove Simple Geometric Theorems Algebraically

On the coordinate grid, points A and B are shown.

Circle C is centered at the origin and passes through (−4,0).

Quadrilateral ABCD is plotted with A(−2,1), B(4,3), C(6,−3), and D(k,−5) (vertices in order).

A line has the equation 3x + 2y = 8.

Consider quadrilateral ABCD with vertices in order:

Select the equation of the line that meets all of the following conditions:

Using the given coordinates, select each statement that, by itself, is sufficient to prove that triangle ABC is a right triangle with the right angle at B.

Let P (3,−1).

A student is trying to prove four points form a square.

Sonia claims: “If a quadrilateral has equal diagonals, then it is a rectangle.”