Prove Quadrilaterals in the Coordinate Plane

Determine the quadrilateral's most specific classification using the distance formula:

A(-5, 8), B(-2, 14), C(12, 7), D(9, 1)

• Parallelogram

• Rectangle

• Rhombus

• Square

You can prove both pairs of opposite sides are parallel by using the slope formula.

• True

• False

Classify the quadrilateral:

K(5, -3), L(7, 1), M(9, -3), N(7, -7)

• Parallelogram

• Rectangle

• Square

• Rhombus

• Did not complete this problem.

Prove that the quadrilateral with vertices at (2,3), (5,7), (8,5), and (5,1) is a parallelogram.

• Calculate the area of the quadrilateral and show that it is equal to zero.

• Calculate the slopes of the opposite sides and show that they are equal.

• Prove that the diagonals bisect each other.

• Show that the opposite angles are equal.

• Find the length of all 4 sides.

• Find the length of both diagonals.

• Find the slope of both diagonals

• Find the slope of all 4 sides.

• mAB ∙ mBC = -1

• AB = CD

• AB = BC

• mAB = mBC

Brad proved that ABCD is a parallelogram by proving both sets of opposite sides to be parallel. What should he do next if he wants to prove it is a rhombus?

• Find the distance of each line to see if they are congruent. 

• Compare the slopes of adjacent sides to see if they are perpendicular. 

Brad proved that ABCD is a parallelogram and that all sides had the same distance What should he do next if he wants to prove it is a square?

• He doesn't need to do anything else, it looks like a square so he is all set. 

• Compare the slopes of adjacent sides to see if they are perpendicular. 

1

• Find the lengths of the diagonals.

• Find the slope of each diagonal.

• Find the midpoint of each diagonal.

• Find the midpoint of each side.

Which of the following will be an accurate ANALYSIS?

• Opposite sides are equal and parallel. All right angles.

• Opposite sides are equal and parallel. No right angles.

• All sides are equal. All right angles.

• All sides are equal. No right angles.