CC Coordinate Algebra
Unit 6 – Connecting Algebra and Geometry Though Coordinates
Test – Day 73
Unit 6 - Free Response Grade Recovery
Each problem section is worth 4 points.
Quadrilateral ABCD has the vertices: A(8, 7), B(12, 4), C(5, -2), D(1, 1)
Definition: A parallelogram is a quadrilateral with two pairs of opposite sides that parallel.
1. What formula do we use to show sides are parallel?
2. Plot and label the figure. Name 2 pairs of opposite sides.
3. Show with mathematical calculations that these opposite sides
are parallel to prove ABCD is a parallelogram.
Parallelogram EFGH has vertices: E(-12, -4), F(-4, 4), G(-7, 7), H(-15, -1)
Theorem – Both pairs of opposite sides in a parallelogram are congruent.
4. What formula do we use to show sides are congruent?
5. Plot and label the figure. Name 2 pairs of opposite sides.
6. Show with mathematical calculations that these opposite sides
are congruent to prove EFGH is a parallelogram.
7. Calculate the perimeter of Parallelogram EFGH.
8. Calculate the area of Parallelogram EFGH.
CC Coordinate Algebra
Unit 6 – Connecting Algebra and Geometry Though Coordinates
Rectangle EFGH has vertices: E(-12, -4), F(-4, 4), G(-7, 7), H(-15, -1)
Theorem – Both diagonals in a rectangle are congruent.
9. What formula do we use to show sides are congruent?
10. Plot and label the figure. Name 1 pair of diagonals.
11. Show with mathematical calculations that these diagonals
are congruent to prove EFGH is a rectangle.
Rectangle EFGH has vertices: E(-12, -4), F(-4, 4), G(-7, 7), H(-15, -1)
Theorem – A rectangle has 4 right angles.
12. What kind of lines make right angles? What formula do we use to
show these types of lines?
13. Plot and label the figure. Name all four sides.
14. Show with mathematical calculations that adjacent sides
make right angles to prove EFGH is a rectangle.
Rhombus JKLM has vertices: J(19, 14), K(9, 14), L(1, 8), M(11, 8)
Theorem – The diagonals in a rhombus are perpendicular.
15. What formula do we use to prove perpendicular lines?
16. Plot and label the figure. Name the two diagonals.
17. Show with mathematical calculations that the diagonals are
perpendicular to prove JKLM is a Rhombus.
Test – Day 73
CC Coordinate Algebra
Unit 6 – Connecting Algebra and Geometry Though Coordinates
Test – Day 73
Classify triangle ABC according to the length of its sides if A(14, 10), B(7, 5), and C(9, 0).
18. What formula do we use to find the lengths of sides?
10
19. Plot and label the figure. Name the three sides.
9
8
7
20. Show with mathematical calculations the lengths of the sides
and name the triangle accordingly.
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10111213141516
For questions 25-28, use the map to the below
Busy Street is y = x – 4, while Country Road is y = -2x + 3
21. Find the equation of the line that is parallel to Country Road and
passes through the Park.
22. Find the equation of the line that is perpendicular to Busy Street
and passes through the House.
23. Find the midpoint between the Park and the Grocery Store.
24. A gas station partitions the line segment from the School (A) to the Park (B) in a 1:2 ratio. Where is the
gas station?