1. 1. Is the transformation below an isometry? Explain.
Translations
Lesson 9-1
Lesson Quiz
1. Is the transformation below an isometry? Explain.
No; the angles are not congruent.
For Exercises 2 and 3, ABCD is an image of KLMN.
2. Name the images of L and N.
B and D
3. Name the sides that correspond to KL and NK.
AB and DA
Use the diagram below.
4. Find the image of MNV under the translation
(x, y)  (x – 2, y + 5).
M(–5, 4), N(–4, 6), V(–1, 5)
5. Write a rule to describe the translation MNV  WZP.
(x, y)  (x + 4, y + 3)
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2. Write an equation for the line through point A that is perpendicular
Reflections
Lesson 9-2
Check Skills You’ll Need
(For help, go to Lesson 3-7.)
Write an equation for the line through point A that is perpendicular
to the given line.
1. 2. 3.
Check Skills You’ll Need
9-2

3. horizontal line through (1, –2) is y = –2.
Reflections
Lesson 9-2
Check Skills You’ll Need
Solutions
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.
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4. Reflections
Lesson 9-2
A reflection (or flip) is an isometry in which a figure and its image have opposite orientations.
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5. Reflections
Lesson 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
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6. Reflections
Lesson 9-2
In other words,
a point and its reflection image are equidistant from the line of reflection.
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7. Finding a Reflection Image
Reflections
Lesson 9-2
Additional Examples
Finding a Reflection Image
If point P(2, –1), is reflected across the y-axis,
what are the coordinates of its reflection image?
Point P is 2 units right of the
reflection line, the y-axis.
Therefore, the image of P' is
2 units left of the reflection line.
So the coordinates of P'
are (–2, –1).
Quick Check
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8. Drawing Reflection Images
Reflections
Lesson 9-2
Additional Examples
Drawing Reflection Images
XYZ has vertices X(0, 3), Y(2, 0), and Z(4, 2). Draw XYZ and its reflection image in the line x = 4.
First locate vertices X, Y, and Z and draw XYZ in a coordinate plane.
Draw the reflection image X Y Z .
Locate points X , Y , and Z such that the line of reflection x = 4 is the perpendicular bisector of XX , YY , and ZZ .
Quick Check
9-2

9. Real-World Connection
Reflections
Lesson 9-2
Additional Examples
Real-World Connection
Show that PD and PW form congruent angles with line .
Because a reflection is an isometry, PD and
PD 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.
Quick Check
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10. Find the coordinates of the image point for each given point and
Reflections
Lesson 9-2
Lesson Quiz
Find the coordinates of the image point for each given point and
reflection line.
1. R(4, –5) across x = –2
2. S(–11, 2) across y = 1
3. T(0, 5) across x-axis
R'(–8, –5)
S'(–11, 0)
T'(0, 5)
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
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