1. Five-Minute Check (over Chapter 2) Mathematical Practices Then/Now
New Vocabulary
Key Concept: Reflection in a Line
Example 1: Reflect a Figure in a Line
Example 2: Minimize Distance by Using a Reflection
Example 3: Reflect a Figure in a Horizontal or Vertical Line
Key Concept: Reflection in the x- or y-axis
Example 4: Reflect a Figure in the x- or y-axis
Key Concept: Reflection in Line y = x
Example 5: Reflect a Figure in the Line y = x
Concept Summary: Reflection in the Coordinate Plane
Lesson Menu

2. Make a conjecture about the next number in the sequence, 5, 20, 80, 320.
D. 1580
5-Minute Check 1

3. B. If you live in Massachusetts, then you do not live in Boston.
Write the contrapositive of this statement. If you live in Boston, then you live in Massachusetts.
A. If you do not live in Massachusetts, then you do not live in Boston.
B. If you live in Massachusetts, then you do not live in Boston.
C. If you do not live in Massachusetts, then you live in Boston.
D. You might live in Massachusetts or Boston.
5-Minute Check 2

4. A. consecutive interior angles B. corresponding angles
What is the special name given to the pair of angles shown by 2 and 6?
A. consecutive interior angles
B. corresponding angles
C. complementary angles
D. supplementary
5-Minute Check 3

5. Find m3.
A. 118
B. 108
C. 62
D. 52
5-Minute Check 4

6. Find the slope of the line that contains the points at (4, 4) and (2, –5).B. C. D.
5-Minute Check 5

7. The measures of two complementary angles are x + 54 and 2x
The measures of two complementary angles are x + 54 and 2x. What is the measure of the smaller angle?
A. 24
B. 42
C. 68
D. 84
5-Minute Check 6

8. Mathematical Practices 5 Use appropriate tools strategically.
Content Standards
G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. MP

9. Describe the effects of reflections on the coordinate plane.
You identified reflections and verified them as congruence transformations.
Given a geometric figure and a reflection, draw the transformed figure.
Describe the effects of reflections on the coordinate plane.
Then/Now

10. line of reflection
Vocabulary

11. Concept

12. Reflect a Figure in a Line
Draw the reflected image of quadrilateral WXYZ in line p using a ruler.
Step 1 Draw segments perpendicular to line p from each point W, X, Y, and Z.
Step 2 Locate W', X', Y', and Z' so that line p is the perpendicular bisector of Points W', X', Y', and Z' are the respective images of W, X, Y, and Z.
Example 1

13. Step 3 Connect vertices W', X', Y', and Z'.
Reflect a Figure in a Line
Step 3 Connect vertices W', X', Y', and Z'.
Answer: Since points W', X', Y', and Z' are the images of points W, X, Y, and Z under reflection in line p, then quadrilateral W'X'Y'Z' is the reflection of quadrilateral WXYZ in line p.
Example 1

14. Draw the reflected image of quadrilateral ABCD in line n.
Example 1

15. Minimize Distance by Using a Reflection
BILLIARDS Suppose that you must bounce the cue ball off side A before it rolls into the pocket at B. Locate the point C along side A that the ball must hit to ensure that it will roll directly toward the pocket.
Example 2

16. Minimize Distance by Using a Reflection
Understand You are asked to locate a point C on side A such that the cue ball will bounce off to roll into the pocket at point B.
Plan For the cue ball to roll into the pocket at B, it must hit point C on side A somewhere in between where it sits now and the pocket at B. Use the reflection of point B on the continuation of the line that B lies on to help find this point.
Example 2

17. Minimize Distance by Using a Reflection
Solve Draw point such that the corner pocket is the midpoint between B and B'.
Connect the cue ball with B' using a line. Locate point C at the intersection of the line drawn and side A.
Example 2

18. Check Check that BC  B'C so that ΔBCB' is an isosceles triangle.
Minimize Distance by Using a Reflection
Answer:
Check Check that BC  B'C so that ΔBCB' is an isosceles triangle.
Example 2

19. A. Determine how far the obstructing wall is from the ball.
MINIATURE GOLF Omar is playing miniature golf at a local course. Because a wall is blocking his direct shot, he needs to bounce the ball off wall W and hit the hole located at point H. Which of these steps would be needed to determine where on wall W Omar should aim?
A. Determine how far the obstructing wall is from the ball.
B. Reflect point H over the line formed by wall W.
C. Determine the exact length of wall W.
D. Find the perpendicular distance from the hole to the wall.
Example 2

20. Reflect a Figure in a Horizontal or Vertical Line
A. Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, –1), and M(0, 1). Graph JKLM and its reflection over x = 1.
Example 3

21. Reflect a Figure in a Horizontal or Vertical Line
Find a corresponding point for each vertex so that a vertex and its image are equidistant from the line x = 1.
Answer:
Example 3

22. Reflect a Figure in a Horizontal or Vertical Line
B. Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, –1), and M(0, 1). Graph JKLM and its reflection over y = –2.
Example 3

23. Reflect a Figure in a Horizontal or Vertical Line
Find a corresponding point for each vertex so that a vertex and its image are equidistant from the line y = –2.
Answer:
Example 3

24. A. Quadrilateral ABCD has vertices A(1, 2), B(0, 1), C(1, –2), and D(3, 0). Graph ABCD and its image over x = 2.
A. B.
C. D.
Example 3

25. B. Quadrilateral WXYZ has vertices W(2, 4), X(3, 3), Y(2, 0), and Z(0, 2). Graph WXYZ and its image over y = –1.
A. B.
C. D.
Example 3

26. Concept

27. Reflect a Figure in the x- or y-axis
A. Given quadrilateral A(1, 1), B(3, 2), C(4, –1), and D(2, –3) and its image A′(1, –1), B′(3, –2), C′(4, 1), and D ′(2, 3), describe the transformation using coordinate notation.
A(1, 1) → A′(1, –1)
B(3, 2) → B′(3, –2)
C(4, –1) → C′(4, 1)
D(2, –3) → D′(2, 3)
Answer: (x, y) → (x, –y). The transformation is a reflection in the x-axis.
Example 4

28. Multiply the x-coordinate of each vertex by –1. (x, y) → (–x, y)
Reflect a Figure in the x- or y-axis
B. Graph quadrilateral ABCD and its image under a reflection in the y -axis.
Multiply the x-coordinate of each vertex by –1.
(x, y) → (–x, y)
A(1, 1) → A'(–1, 1) B(3, 2) → B'(–3, 2) C(4, –1) → C'(–4, –1) D(2, –3) → D'(–2, –3)
Example 4

29. Reflect a Figure in the x- or y-axis
Answer:
Example 4

30. A. Graph quadrilateral LMNO with vertices L(3, 1), M(5, 2), N(6, –1), and O(4, –3) and its reflected image in the x-axis. Select the correct coordinates for the new quadrilateral L'M'N'O'.
A. L'(3, –1), M'(5, –2), N'(6, 1), O'(4, 3)
B. L'(–3, 1), M'(–5, 2), N'(–6, –1), O'(–4, –3)
C. L'(–3, –1), M'(–5, –2), N'(–6, 1), O'(–4, 3)
D. L'(1, 3), M'(2, 5), N'(–1, 6), O'(–3, 4)
Example 4

31. B. Graph quadrilateral LMNO with vertices L(–1, 0), M(1, 1), N(2, –2), and O(0, –4) and its reflected image under the y-axis. Select the correct coordinates for the point M' in the new quadrilateral L'M'N'O'.
A. L'(–1, 0), M'(1, –1), N'(2, 2), O'(0, 4)
B. L'(1, 0), M'(–1, 1), N'(–2, –2), O'(0, –4)
C. L'(1, 0), M'(–1, –1), N'(–2, 2), O'(0, 4)
D. L'(0, –1), M'(1, 1), N'(–2, 2), O'(–4, 0)
Example 4

32. Concept

33. Interchange the x- and y-coordinates of each vertex. (x, y) → (y, x)
Reflect a Figure in the Line y = x
Quadrilateral ABCD with vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection of the line y = x.
Interchange the x- and y-coordinates of each vertex.
(x, y) → (y, x)
A(1, 1) → A'(1, 1) B(3, 2) → B'(2, 3) C(4, –1) → C'(–1, 4) D(2, –3) → D'(–3, 2)
Example 5

34. Reflect a Figure in the Line y = x
Answer:
Example 5

35. Quadrilateral EFGH has vertices E(–3, 1), F(–1, 3), G(1, 2), and H(–3, –1). Graph EFGH and its image under reflection of the line y = x. Select the correct coordinates for the point H' in the new quadrilateral E'F'G'H'.
A. E'(–3, –1), F'(–1, –3), G'(1, –2), H'(–3, 1)
B. E'(3, –1), F'(1, –3), G'(–1, 2), H'(3, –1)
C. E'(1, –3), F'(3, –1), G'(2, 1), H'(–1, –3)
D. E'(–1, 3), F'(–3, 1), G'(–2, –1), H'(1, 3)
Example 5

36. Concept