Geometry 6-8 Applying Coordinate Geometry

by Matthew Richardson

| 21 QuestionsNote from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

1

10 pts

Solve It! The points shown are three vertices of a parallelogram. Draw all the possible locations of D, the fourth vertex?

2

2

10 pts

Problem 1 Got It?

A

B

C

D

3

3

10 pts

Problem 1 Got It?

A

B

C

D

4

5

5

10 pts

Problem 2 Got It. The diagram shows a trapezoid with the base centered at the origin. Is the trapezoid isosceles? Explain.

6

6

10 pts

Problem 3 Got It? Plan a coordinate proof of the Triangle Midsegment Theorem (Theorem 5-1).

7

7

10 pts

A

B

C

D

8

8

10 pts

A

B

9

9

10 pts

A

B

C

D

10

10 pts

Reasoning: How do variable coordinates generalize figures in the coordinate plane? For example, what do you know about (3, a), (b, -5), etc.

11

10 pts

Reasoning: A vertex of a quadrilateral has coordinates (a, b). The x-coordinates of the other three vertices are a or -a and the y-coordinates are b or -b. What kind of quadrilateral is the figure? Be as specific as possible.

The quadrilateral is a rectangle.

The quadrilateral is a rhombus.

The quadrilateral is a square.

12

12

10 pts

Error Analysis: A classmate says the endpoints of the midsegment of the trapezoid in Problem 3 are as follows.

What is your classmate's error? Explain.

13

10 pts

Review Lesson 6-7: Let X(-2, 3), Y(5, 5), and Z(4, 10) be the vertices of a triangle. Is △XYZ a right triangle? Explain.

14

10 pts

Review Lesson 2-2: Write the inverse of the statement.

If x = 51, then 2x = 102.

15

10 pts

Review Lesson 2-2: Write the converse of the statement.

If x = 51, then 2x = 102.

16

10 pts

Review Lesson 2-2: Write the contrapositive of the statement.

If x = 51, then 2x = 102.

17

10 pts

Review Lesson 3-7: Find and graph the equation of the line that contains the origin and (4, 5).

18

10 pts

Review Lesson 3-7: Find the equation of the line that contains (p, q) and has slope a/b.

y - p = (a/b)(x - q)

y - q = (a/b)(x - p)

y - a = (p/q)(x - b)

y - b = (p/q)(x - a)

19

10 pts

Vocabulary Review: Categorize each statement as true or false.

- True
- False

- The vertex of an angle is the endpoint of two rays.
- When you name angles using three points, the vertex gets named first.
- A polygon has the same number of sides and vertices.

20

20

10 pts

Use Your Vocabulary: Match each point with its coordinates.

- A
- B
- C
- D

- (-1, -3)
- (1, 3)
- (3, -1)
- (-3, 1)

21

10 pts

Reflection: Math Success

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