featurelesson geometry lesson main 1. is the transformation below an isometry? explain. no; the...
TRANSCRIPT
FeatureLesson
GeometryGeometry
LessonMain
1. Is the transformation below an isometry? Explain.
No; the angles are not congruent.
Lesson 9-1
TranslationsTranslations
For Exercises 2 and 3, ABCD is an image of KLMN.
B and D
AB and DA
2. Name the images of L and N.
3. Name the sides that correspond to KL and NK.Use the diagram below.
5. Write a rule to describe the translation MNV WZP.
4. Find the image of MNV under the translationM(–5, 4), N(–4, 6), V(–1, 5)(x, y) (x – 2, y + 5).
(x, y) (x + 4, y + 3)
Lesson Quiz
9-2
FeatureLesson
GeometryGeometry
LessonMain
Lesson 9-2
(For help, go to Lesson 3-7.)
Write an equation for the line through point A that is perpendicularto the given line.
1. 2.
ReflectionsReflections
3.
Check Skills You’ll Need
Check Skills You’ll Need
9-2
FeatureLesson
GeometryGeometry
LessonMain
Solutions
Lesson 9-2
ReflectionsReflections
1. A line perpendicular to a vertical line is a horizontal line. The equation of the horizontal line through (1, –2) is y = –2.
2. A line perpendicular to a horizontal line is a vertical line. The equation of the vertical line through (–1, –1) is x = –1.
3. The given line has slope 1. A line perpendicular to a line with slope 1 has a slope of –1. The equation of a lien with slope –1 through (–1, 2) is y = –x + 1.
Check Skills You’ll Need
9-2
FeatureLesson
GeometryGeometry
LessonMain
Lesson 9-2
ReflectionsReflections
9-2
A reflection (or flip) is an isometry in which a figure and its image have opposite orientations.
FeatureLesson
GeometryGeometry
LessonMain
Lesson 9-2
ReflectionsReflections
9-2
You can use the following two rules to reflect a figure across a line r.
•If a point A is on line r, then the image of A is A itself (that is, A’ = A).
•If a point B is not on line r, then r is the perpendicular bisector of .'BB
FeatureLesson
GeometryGeometry
LessonMain
Lesson 9-2
ReflectionsReflections
9-2
In other words,
a point and its reflection image are equidistant from the line of reflection.
FeatureLesson
GeometryGeometry
LessonMain
If point P(2, –1), is reflected across the y-axis,what are the coordinates of its reflection image?
Lesson 9-2
ReflectionsReflections
So the coordinates of P'are (–2, –1).
Quick Check
Point P is 2 units right of thereflection line, the y-axis.Therefore, the image of P' is2 units left of the reflection line.
Additional Examples
9-2
Finding a Reflection Image
FeatureLesson
GeometryGeometry
LessonMain
First locate vertices X, Y, and Z and draw XYZ in a coordinate plane.
Locate points X , Y , and Z such that the line of reflection x = 4 is the perpendicular bisector of XX , YY , and ZZ .
Draw the reflection image X Y Z .
XYZ has vertices X(0, 3), Y(2, 0), and Z(4, 2). Draw XYZ
and its reflection image in the line x = 4.
Lesson 9-2
ReflectionsReflections
Quick Check
Additional Examples
9-2
Drawing Reflection Images
FeatureLesson
GeometryGeometry
LessonMain
Show that PD and PW form congruent angles with line .
PD and PW also form congruent angles with line because vertical angles are congruent.
Therefore, PD and PW form congruent angles with line by the Transitive Property.
Lesson 9-2
ReflectionsReflections
Quick Check
Additional Examples
Because a reflection is an isometry, PD andPD form congruent angles with line .
9-2
Real-World Connection
FeatureLesson
GeometryGeometry
LessonMain
Find the coordinates of the image point for each given point andreflection line.
1. R(4, –5) across x = –2
2. S(–11, 2) across y = 1
3. T(0, 5) across x-axis
Lesson 9-2
ReflectionsReflections
XYZ has vertices X(–2, 3), Y(1, 1), and Z(2, 4). Draw XYZ and its reflection image in each line.
4. the x-axis 5. the line x = 5
R'(–8, –5)
S'(–11, 0)
T'(0, 5)
Lesson Quiz
9-2