Coordinate Proofs

Analyze the graph. Using distance formula, can you prove this is a rectangle?

• Yes, because AD = BC = 10 and AB = CD = 5

• Yes because AD = BC = 5 and AB = CD = 10

Analyze the graph. Can you prove this is a rectangle using slope?

Analyze the graph. Using distance formula, can you prove this is a rhombus?

• Yes all of the sides have a length of 5

Sarah proved that this is a square. The slopes of -2/5 and 5/2 made her able to do this. How come?

• Because those slopes form parallel lines.

• Because those slopes form perpendicular lines, creating right angles.

• Because those slopes make the sides congruent.

Prove the shape is a trapezoid.

• The slope of the parallel bases is 4/3

• The slope of the parallel bases is -4/3

• It is not a trapezoid because the slopes do not match.

• It is not a trapezoid because the legs are not parallel.

You have plotted the parallelogram in the picture. What is the slope of line BC without having to use the slope formula?

• 0

• Undefined

You have plotted the parallelogram in the picture. Which sides would you want to find the slope of first?

• AB and BC

• AB and AD

• AD and DC

• AB and DC

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. 

Use the distance formula to see if side AB is congruent to side BC.

• Yes they are congruent

• No, they are not congruent

Use the distance formula to see if side BC is congruent to side AD.

• Yes they are congruent

• No, they are not congruent