Proving Quadrilaterals in the Coordinate Plane

Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply.

A(-10, 4), B(-2, 10), C(4, 2), D(-4, -4)

• rhombus

• rectangle

• square

• not enough information

Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply.

J(-9, -7), K(-4, -2), L(3, -3), M(-2, -8)

• rectangle

• rhombus

• square

• not enough information

Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply.

W(-2, 5), X(5, 5), Y(5, 0), Z(-2, 0)

• rectangle

• rhombus

• square

• not enough information

The coordinates of three vertices of a parallelogram ABCD are given. Find the coordinates of the 4th point so that the given type of figure is formed.

A(4, -2), B(-5, -2), D(4, 4), rectangle

• (-5, 4)

• (-2, 4)

• (2, 5)

• (5, -4)

The coordinates of three vertices of a parallelogram ABCD are given. Find the coordinates of the 4th point so that the given type of figure is formed.

A(0, 2), B(4, -2), C(0, -6), square

• (4, 2)

• (2, 0)

• (-6, 0)

• (-4, -2)

The coordinates of three vertices of a parallelogram ABCD are given. Find the coordinates of the 4th point so that the given type of figure is formed.

A(-5, 5), B(0, 0), C(7, 1), rhombus

• (2, 6)

• (2, 0)

• (2, 1)

• (5, -5)

The coordinates of three vertices of a parallelogram ABCD are given. Find the coordinates of the 4th point so that the given type of figure is formed.

A(2, 1), B(-1, 5), C(-5, 2), square

• (1, 2)

• (-2, -2)

• (2, 1)

• (2, -5)

A parallelogram has vertices at (0, 0), (5, 6), and (10, 0). Which could be the fourth vertex of the parallelogram? Select all that apply.

• (5, -6)

• (15, 6)

• (0, -6)

• (10, 6)

• (-5, 6)

Which formula is used to show that lengths are parallel or perpendicular?

• Slope

• Midpoint

• Distance

Which formula is used to show that lengths are equal?

• Slope

• Midpoint

• Distance