1. Lesson 10-5: Transformations
Gr. 7 Geometry
Reflections
Lesson 10-5: Transformations

2. Lesson 10-5: Transformations
Re-cap
What is a translation?
Lesson 10-5: Transformations

3. Review: 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. .
Lesson 10-5: Transformations

4. Lesson 10-5: Transformations
Reflections
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 . l
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

5. Reflections – continued…
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 : n l
reflects across the y axis to line n
(2, 1)  (-2, 1) & (5, 4)  (-5, 4)
reflects across the x axis to line m.
(2, 1)  (2, -1) & (5, 4)  (5, -4) m
Lesson 10-5: Transformations

6. 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.
Example:
Reflect the fig. across the line y = 1.
(2, 3)  (2, -1).
(-3, 6)  (-3, -4)
(-6, 2)  (-6, 0)
Lesson 10-5: Transformations

7. Lesson 10-5: Transformations
Lines of Symmetry
If a line can be drawn through a figure so the one side of the figure is a reflection of the other side, the line is called a “line of symmetry.”
Some figures have 1 or more lines of symmetry.
Some have no lines of symmetry.
Four lines of symmetry
One line of symmetry
Two lines of symmetry
Infinite lines of symmetry
No lines of symmetry
Lesson 10-5: Transformations

8. Composite Reflections
If an image is reflected over a line and then that image is reflected over a parallel line (called a composite reflection), it results in a translation.
Example: C B A
Image A reflects to image B, which then reflects to image C. Image C is a translation of image A
Lesson 10-5: Transformations

9. As the video is playing, take jot notes
Lesson 10-5: Transformations