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

On the coordinate grid, points A(−2, 6), B(8, −2), and C(3, 2) are plotted.

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

Quadrilateral ABCD has vertices A(−2,1), B(4,3), C(6,−3), and D(k,−5), listed 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.

Point P(1, 2) and point Q(5, 2) are adjacent vertices of a square.

A student is trying to determine whether four points form a square.

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