Practicing with
Proofs in Coordinate Geometry

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Answer the following problems dealing with
Coordinate Geometry proofs.

(Please Note:  Answers will show only ONE possible solution to a problem.
 Even when a specific method of solution is requested, answers may vary in presentation.)

Before you begin, refresh your memory ...

Distance Formula


 

Slope Formula

 
Midpoint Formula

 

When developing a coordinate geometry proof:

1.  draw and label the graph
2.  state the formulas you will be using
3.  show ALL work (if you are using your graphing calculator, be sure to show your screen displays as part of your work.)
4.  have a concluding sentence stating
what you have proven and why it is true.


 

1.

Prove that quadrilateral A(1,2), B(2,5), C(5,7) and D(4,4) is a parallelogram by using slopes.

Proof


 

2.

Prove that A(1,1), B(4,4), C(6,2) are the vertices of a right triangle.

Proof

 
 

3.

Prove that quadrilateral A(1,-2), B(13,4),
C(6,8) and D(-2,4) is a trapezoid, but is NOT an isosceles trapezoid.

Proof



 

4.

Prove that A(-2,2), B(1,4), C(2,8) and D(-1,6) is a parallelogram using midpoints.

Proof

 

 

5.

Prove that A(-3,2), B(-2,6), C(2,7)
and D(1,3) is a rhombus.

Proof

 

 

6.

Prove that A(4,-1), B(5,6), C(1,3) is an isosceles right triangle.

Proof

 

 

7.

Guinevere and Lancelot see a drawing of quadrilateral ABCD,  A(2,2), B(5,-2),
C(9,1) and D(6,5).
Guinevere says the figure is a rhombus, but not a square.  Lancelot says the figure is a square.  Write a proof to show who is making the correct observation.

Proof