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Warm Up Write a conjecture of what is
going on in the picture
UNIT 2Segment1:Transformation
Lesson:2.1 Reflection
Essential Question: Explain How isometry correlates with reflection
Lesson 10-5: Transformations
Isometry
AKA: congruence transformation
a transformation in which an original figure and its image are congruent.
Types of Transformations
Reflections: These are like mirror images as seen across a line or a point.
Translations ( or slides): This moves the figure to a new location with no change to the looks of the figure.
Rotations: This turns the figure clockwise or counter-clockwise but doesn’t change the figure.
Dilations: This reduces or enlarges the figure to a similar figure.
Lesson 10-5: Transformations
Pre-Image: original figure
Image: after transformation. Use prime notation
Notation:
A
A’
B
B’
C
C ’
Reflections
You could fold the picture along line l and the left figure would coincide with the corresponding parts of right figure.
Lesson 10-5: Transformations
l
You can reflect a figure using a line or a point. All measures (lines and angles) are preserved but in a mirror image.
Example: The figure is reflected across line l .
Properties of reflections
PRESERVE
Size (area, length, perimeter…)
Shape
CHANGE
orientation (flipped)
Reflect x-axis: (a, b) -> (a,-b)
Change sign y-coordinate
Reflect y-axis: (a, b) -> (-a, b)Change sign on x coordinate
Reflections – continued…
reflects across the y axis to line n
(2, 1) (-2, 1) & (5, 4) (-5, 4)
Lesson 10-5: Transformations
Reflection across the x-axis: the x values stay the same and the y values change sign. (x , y) (x, -y)
Reflection across the y-axis: the y values stay the same and the x values change sign. (x , y) (-x, y)
Example: In this figure, line l :
reflects across the x axis to line m.
(2, 1) (2, -1) & (5, 4) (5, -4)
ln
m
Reflections across specific lines:
To reflect a figure across the line y = a or x = a, mark the corresponding points equidistant from the line.
i.e. If a point is 2 units above the line its corresponding image point must be 2 points below the line.
Lesson 10-5: Transformations
(-3, 6) (-3, -4)
(-6, 2) (-6, 0)
(2, 3) (2, -1).
Example:
Reflect the fig. across the line y = 1.
PARTNER SWAP:Part I: (Live under my rules)
Use graphing paper to graph a triangle label 3 pointsSwap with your partner
Have him reflect over y=xWRITE a conjecture about how (a, b) will be changed after reflecting over y = x. Explain.
Repeat by reflecting over the line y = -x. Write a conjecture.
PARTNER SWAP:Part I: (Live under my rules)
Use graphing paper to graph a triangle label 3 pointsSwap with your partner
Have him reflect over y=xWRITE a conjecture about how (a, b) will be changed after reflecting over y = x. Explain.
Repeat by reflecting over the line y = -x. Write a conjecture.
Homework
Complete the Vocabulary
Pg 481
1-21 odd 24,25 and 26
Lesson 10-5: Transformations
