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Lesson Menu

Five-Minute Check (over Chapter 8) Then/Now New

Vocabulary Key Concept Reflection in a

Line Example 1 Reflect a Figure in a

Line Example 2 Real-World Example 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

5-Minute Check 1

Find the geometric mean between 8 and 15. State

the exact answer.

5-Minute Check 2

Determine whether the numbers 6, 9, and 12 are

the measures of the sides of a right triangle.

A. yes B. no

5-Minute Check 3

Find cos A for ?ABC if m?C 90, AB x, AC y,

and CB z.

5-Minute Check 4

Find sin A for ?ABC if m?C 90, AB x, AC y,

and CB z.

5-Minute Check 5

Find tan B for ?ABC if m?C 90, AB x, AC y,

and CB z.

5-Minute Check 6

If m?A 42, AB 7, and BC 6 in ?ABC, what is

m?B?

A. 26.5 B. 35.0 C. 51.3 D. 86.7

Then/Now

You identified reflections and verified them as

congruence transformations. (Lesson 47)

- Draw reflections.

- Draw reflections in the coordinate plane.

Vocabulary

- line of reflection

Concept

Example 1

Reflect a Figure in a Line

Draw the reflected image of quadrilateral WXYZ in

line p.

Step 1 Draw segments perpendicular to line p

from each point W, X, Y, and Z.

Example 1

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

Draw the reflected image of quadrilateral ABCD in

line n.

Example 2

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

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

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

Minimize Distance by Using a Reflection

Answer

Example 2

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 3

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

image over x 1.

Example 3

Reflect a Figure in a Horizontal or Vertical Line

Use the horizontal grid lines to find a

corresponding point for each vertex so that each

vertex and its image are equidistant from the

line x 1.

Answer

Example 3

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

image over y 2.

Example 3

Reflect a Figure in a Horizontal or Vertical Line

Use the vertical grid lines to find a

corresponding point for each vertex so that each

vertex and its image are equidistant from the

line y 2.

Answer

Example 3

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.

Example 3

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.

Concept

Example 4

Reflect a Figure in the x- or y-axis

A. Graph quadrilateral ABCD with vertices A(1,

1), B(3, 2), C(4, 1), and D(2, 3) and its image

reflected in the x-axis.

Multiply the y-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

Reflect a Figure in the x- or y-axis

Answer

Example 4

Reflect a Figure in the x- or y-axis

B. Graph quadrilateral ABCD with vertices A(1,

1), B(3, 2), C(4, 1), and D(2, 3) and its

reflected image 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

Reflect a Figure in the x- or y-axis

Answer

Example 4

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

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)

Concept

Example 5

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

Reflect a Figure in the Line y x

Answer

Example 5

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)

Concept

End of the Lesson