GPS Geometry
Name: _____________________________________________________________________________ Date: _____________________________
Connecting Algebra & Geometry through Coordinates: Parallelograms and Rectangles
Answer the following questions. Show your work on another sheet of paper. LABEL ALL POINTS!
1.
Plot and label each point. A(1,2), B(2, 5), C(5, 7) and D(4, 4)
2.
Which quadrilateral(s) does this look like? _______________________________________
3.
Prove the quadrilateral is a parallelogram by using slopes.
Slope Formula:
𝑦2 −𝑦1
𝑥2 −𝑥
̅̅̅̅
Slope of 𝐴𝐵
̅̅̅̅
Slope of 𝐵𝐶
Slope of ̅̅̅̅
𝐷𝐶
̅̅̅̅
Slope of 𝐴𝐷
4.
Based on the slopes of the shape what do you think this shape is? Was your guess in #2 correct?
5.
What conclusions can you make about the opposite angles?
6.
What conclusions can you make about the consecutive angles?
7.
What conclusions can you make about the diagonals?
8.
Plot and label each point. A(0,0), B(5, 2), C(6, 5) and D(1, 3)
9.
Which quadrilateral(s) does this look like? _____________________________________
Slope of ̅̅̅̅
𝐴𝐵
̅̅̅̅
Slope of 𝐵𝐶
Slope of ̅̅̅̅
𝐷𝐶
̅̅̅̅
Slope of 𝐴𝐷
̅̅̅̅ ? _____________ Is the slope of 𝐷𝐶
̅̅̅̅ the same as ̅̅̅̅
10. Is the slope of ̅̅̅̅
𝐴𝐵 the same as 𝐵𝐶
𝐴𝐵 ?________________. What
does this indicate the shape could be?
11. Using the distance formula 𝑑 = √(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦)2 how long is ̅̅̅̅
𝐷𝐶 ? _________ How long is side ̅̅̅̅
𝐴𝐵 ? ______
̅̅̅̅?__________ How about ̅̅̅̅
How long is side 𝐴𝐷
𝐵𝐶 ?____________ Does this narrow down which shape this could be?
̅̅̅̅ and 𝐵𝐶
̅̅̅̅ . Are these slopes opposite reciprocals of each other? __________ This answer
12. Compare the slopes of 𝐴𝐷
should tell you which shape you have on the coordinate plane. What is the shape? ________________________
GPS Geometry
13. Plot and label each point. A(-3, 0), B(-2, 3), C(4, 1) and D(3, -2)
14. Which quadrilateral(x) does this look like? ___________________________________
15. Find the length of each side and both diagonals to the nearest tenth.
AB = ______
BC = ______
AC = ______
DC = ______
DA = ______
BD = ______
16. What conclusions can you make about the opposite sides?
17. Find the slope of each side.
Slope of AB = ______
Slope of DC = ______
Slope of BC = ______
Slope of AD = ______
18. What conclusions can you make about the opposite slopes?
19. Compare the slope of AB to that of BC. Are they opposite reciprocals?__________________ What does this mean
the shape must be? _________________________________
20. Plot and label each point. A(-1, 4), B(3, 2), C(1, -2), and D(-3, 0)
21. Which quadrilateral(s) does this look like? ___________________________________
22. Find the length of each side to the nearest tenth.
AB = ______
BC = ______
DC = ______
DA = ______
23. What conclusions can you make about the lengths of the opposite sides?
24. Find the slope of each side and both diagonals.
Slope of AB = ______
Slope of DC = ______
Slope of BC = ______
Slope of AD = ______
25. What conclusions can you make about the slope?
26. Compare the slope of AB to that of BC. Are they opposite reciprocals?__________________ What does this mean
the shape must be? _________________________________