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Splash Screen

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Title: Glencoe Geometry Author: Crystal Kestner Last modified by: Crystal Kestner Created Date: 12/6/2007 2:31:51 PM Document presentation format – PowerPoint PPT presentation

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Title: Splash Screen


1
Splash Screen
2
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
3
5-Minute Check 1
Find the geometric mean between 8 and 15. State
the exact answer.
4
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
5-Minute Check 3
Find cos A for ?ABC if m?C 90, AB x, AC y,
and CB z.
6
5-Minute Check 4
Find sin A for ?ABC if m?C 90, AB x, AC y,
and CB z.
7
5-Minute Check 5
Find tan B for ?ABC if m?C 90, AB x, AC y,
and CB z.
8
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
9
Then/Now
You identified reflections and verified them as
congruence transformations. (Lesson 47)
  • Draw reflections.
  • Draw reflections in the coordinate plane.

10
Vocabulary
  • line of reflection

11
Concept
12
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.
13
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.
14
Example 1
Draw the reflected image of quadrilateral ABCD in
line n.
15
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.
16
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.
17
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.
18
Example 2
Minimize Distance by Using a Reflection
Answer
19
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.
20
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.
21
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
22
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.
23
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
24
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.
25
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.
26
Concept
27
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)
28
Example 4
Reflect a Figure in the x- or y-axis
Answer
29
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)
30
Example 4
Reflect a Figure in the x- or y-axis
Answer
31
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)
32
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)
33
Concept
34
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)
35
Example 5
Reflect a Figure in the Line y x
Answer
36
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)
37
Concept
38
End of the Lesson
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