1. No category

6-8
Applying Coordinate
Geometry
Vocabulary
Review
Write T for true or F for false.
1. The vertex of an angle is the endpoint of two rays.
2. When you name angles using three points, the vertex gets named first.
3. A polygon has the same number of sides and vertices.
A
4. Circle the vertex of the largest angle in nABC at the right.
C
5. Circle the figure that has the greatest number of vertices.
hexagon
kite
B
rectangle
trapezoid
Vocabulary Builder
coordinates (noun) koh AWR din its
(Ľ1, 3)
Definition: Coordinates are numbers or letters that
specify the location of an object.
x-coordinate
y-coordinate
Math Usage: The coordinates of a point on a plane are an ordered
d d pair
i off numbers.
b
Main Idea: The first coordinate of an ordered pair is the x-coordinate. The second is
the y-coordinate.
Use Your Vocabulary
Draw a line from each point in Column A to its coordinates
in Column B.
Column A
(21, 23)
7. B
(1, 3)
8. C
(3, 21)
9. D
(23, 1)
Ľ4
Ľ2 O
B
Ľ2
Ľ4
174
y
C
2
A
Column B
6. A
Chapter 6
4
x
2
4
D
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
coordinates
Problem 1 Naming Coordinates
Got It? RECT is a rectangle with height a and length 2b.
The y-axis bisects EC and RT. What are the coordinates
of the vertices of RECT?
10. Use the information in the problem to mark
all segments that are congruent to OT.
11. Rectangle RECT has length
so RT 5
12. The coordinates of O are (
coordinates of R are (2
C
x
O
R
,
and RO 5 OT 5
y
E
T
.
, 0), so the coordinates of T are (
, 0), and the
, 0).
13. Rectangle RECT has height a, so TC 5 RE 5
14. The coordinates of C are (
,
.
), so the coordinates of E are (
,
).
15. Why is it helpful that one side of rectangle RECT is on the x-axis and the figure is
centered on the y-axis.
_______________________________________________________________________
_______________________________________________________________________
Problem 2
y
Using Variable Coordinates
C (2b, 2c)
B(2a à 2b, 2c)
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Got It? Reasoning The diagram at the right shows
a general parallelogram with a vertex at the origin and
one side along the x-axis. Explain why the x-coordinate
of B is the sum of 2a and 2b.
x
O
16. Complete the diagram.
A(2a, 0)
17. Complete the reasoning model below.
Write
Think
Opposite sides of a parallelogram are congruent.
OA â
The x-coordinate is the sum of the lengths in
The x-coordinate of B is
the brackets.
à
â
â
.
18. Explain why the x-coordinate of B is the sum of 2a 1 2b.
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
175
Lesson 6-8
You can use coordinate geometry and algebra to prove theorems in geometry.
This kind of proof is called a coordinate proof.
Problem 3 Planning a Coordinate Proof
Got It? Plan a coordinate proof of the Triangle Midsegment Theorem
(Theorem 5-1).
19. Underline the correct words to complete Theorem 5-1.
If a segment joins the vertices / midpoints of two sides of a triangle, then the
segment is perpendicular / parallel to the third side, and is half its length.
20. Write the coordinates of the vertices of nABC on the grid below. Use multiples of 2
to name the coordinates.
y
B(
F
,
)
E
x
O C(
,
)
A(
,
)
_______________________________________________________________________
_______________________________________________________________________
22. Complete the Given and Prove.
Given: E is the 9 of AB and F is the 9 of BC.
1
Prove: EF 6 AC, and EF 5 2 AC
23. Circle the formula you need to use to prove EF 6 AC. Underline the formula
you need to use to prove EF 5 12 AC.
Distance Formula
Midpoint Formula
Slope Formula
Underline the correct word to complete each sentence.
24. If the slopes of EF and AC are equal, then EF and AC are congruent / parallel .
25. If you know the lengths of EF and AC, then you can add / compare them.
26. Write three steps you must do before writing the plan for a coordinate proof.
_______________________________________________________________________
_______________________________________________________________________
Chapter 6
176
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
21. Reasoning Why should you make the coordinates of A and B multiples of 2?
Lesson Check • Do you UNDERSTAND?
Error Analysis A classmate says the endpoints of the midsegment of the
y
d1a c
b c
trapezoid at the right are Q 2 , 2 R and Q 2 , 2 R . What is your classmate’s
R(2b, 2c)
error? Explain.
M
A(2d, 2c)
N
x
27. What is the Midpoint Formula?
O
M5 a
x1 1 x2 y1 1 y2
,
P(2a, 0)
b
28. Find the midpoint of each segment to find the endpoints of MN.
OR
AP
29. The endpoints of the midsegment are (
,
) and (
,
).
30. How are the endpoints that your classmate found different from the endpoints that
you found in Exercise 28?
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
__________________________________________________________________________
__________________________________________________________________________
31. What is your classmate’s error? Explain.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
coordinate geometry
coordinate proof
variable coordinates
Rate how well you can use properties of special figures.
Need to
review
0
2
4
6
8
Now I
get it!
10
177
Lesson 6-8