MCC8.G.3 Describe the effect of dilations, translations, rotations and reflections on...
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![Page 1: MCC8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.](https://reader038.fdocuments.in/reader038/viewer/2022110404/56649e975503460f94b9a9e4/html5/thumbnails/1.jpg)
Reflection
MCC8.G.3Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
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• One type of transformation uses a line that acts like a mirror, with an image reflected across a line is a reflection and the mirror line is the line of reflection.
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12.2 Reflection (flip)Example A
Quadrilateral ABCD is being reflected across the y-axis.
1. What are the coordinates for quadrilateral ABCD?
Point A (1,1)
Point B (2,3)
Point C (4,4)
Point D (5,2)
2. How far is each point from the line of reflection?
Point A is 1 unit
Point B is 2 units
Point C is 4 units
Point D is 5 units
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12.2 Reflection (flip)Example A
Each vertex should be the same distance from the line of symmetry, just in the opposite position.
REMEMBER:
3. Using the information in question 2, how far should the image be from the line of reflection?
Pre-image
Point A is 1 unit
Point B is 2 units
Point C is 4 units
Point D is 5 units
Image
Point A′ is 1unit
Point B′ is 2 units
Point C′ is 4 units
Point D′ is 5 units
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12.2 Reflection (flip)Example A
4. What are coordinates for quadrilateral A’B’C’D’?
A′ (-1,1)
B′ (-2,3)
C′ (-4,4)
D′ (-5,2)
5. Compare and contrast the coordinates for original and the image?
Pre-image
A (1,1)
B (2,3)
C (4,4)
D (5,2)
Image
A′ (-1,1)
B′ (-2,3)
C′ (-4,4)
D′ (-5,2)
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12.2 Reflection (flip)Example B
This time the original is being reflected over the x-axis.
Write down the coordinates for the original and the image. Compare and contrast the coordinates?
Pre-Image
F (2,3)
G (4,1)
H (1,0)
Image
F′ (2,-3)
G′ (4,-1)
H′ (1,0)
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When you reflect over the x-axis the x-coordinates stay the same and the y-coordinates change to its opposite.
When you reflect over the y-axis the x-coordinates change to its opposite and the y-coordinates stay the same.
What to remember…
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• Reflection- the figure is flipped over a line.
Reflection over the x-axis:(x, y) (x, -y)
Reflection over the y-axis:(x, y) (-x, y)
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What happens if the line of reflection is not the axis?
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Reflections in other lines . . .• Let’s look at what happens if you reflect a figure across the
line y = x or line y = -x
y = x y = -x
Look at corresponding points. Notice that for (x, y), the corresponding image point is (y, x). For (-2, 5), image point is (5, -2).
Look at corresponding points. Notice that for (x, y), the corresponding image point is (-y, -x). For (6, 3), image point is (-3, -6)
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What does y=a look like?• a represents any number.Let’s graph y = 3
What type of line did you graph?Horizontal line
y = 3x y (x,y)-2 3 (-2,3)1 3 (1,3)4 3 (4,3)
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What does x=c look like?• c represents any number.Let’s graph x = -2
What type of line did you graph?Vertical line
x = -2x y (x,y)-2 5 (-2,5)-2 0 (-2,0)-2 -3 (-2,-3)
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Reflections in more lines . . .• What happens if you reflect in a line
y = 3? or x = -2 ?
Each point and corresponding image must be equidistant from the line. Note A (4, 2) and image point A′(4, 4) are each 1 unit from the line y = 3.
Each point and corresponding image must be equidistant from the line. Note B (0, 4) and image point B′(-4, 4) are 2 units from the line x = -2.
y = 3 A
A’
x = -2
BB’
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Steps to finding the image coordinates 1. Determine if the figure will reflect
horizontally or vertically. This will tell you which coordinate will change.
Since it Y=3 only the y-coordinate will change.
2. Find the distance between the pre-image coordinate and the line of reflection by subtracting the coordinate from the value of the line.
U (-3, 5)
5 – 3 = 2U is 2 units above y=3
So how far should U′ be the line of reflection?2 units below
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Steps to finding the image coordinates 3. Since it should be below, subtract the
distance from the value of the line of reflection.
4. Check by graphing
U (-3,5)U′ should be 2 units belowLine of reflection y=3
3-2 = 1
So U′ should be at (-3,1)
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Reteach Video next
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ReflectionReflection
Reflect ABC across the x-axis.Reflect ABC across the x-axis.
4 Units3 Units
A
B
C
4 Units
A’
3 Units
B’
1 Unit
1 UnitC’
Count the number of units point A is from the line of reflection.Count the same number of units on the other side and plot point A’.
Count the number of units point B is from the line of reflection.Count the same number of units on the other side and plot point B’.
Count the number of units point C is from the line of reflection.Count the same number of units on the other side and plot point C’.
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Reflections in a line• Reflections can be made across the x-axis.
Look at the corresponding points in the figures. The point (-4, 4) corresponds to the image point (-4, -4). The point (2, 4) corresponds to (2, -4).
Notice that in a reflection over the x-axis, the coordinates of the x’s stay the same but the y’s change sign.
In a reflection across the x-axis, the point (x, y) reflects onto image (x, -y).
x-axis
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ReflectionReflection
Reflect ABC across the y-axis.Reflect ABC across the y-axis.
5 Units
2 UnitsA
B
C
5 Units A’
2 Units
B’
3 Units 3 UnitsC’
Count the number of units point A is from the line of reflection.Count the same number of units on the other side and plot point A’.
Count the number of units point B is from the line of reflection.Count the same number of units on the other side and plot point B’.
Count the number of units point C is from the line of reflection.Count the same number of units on the other side and plot point C’.
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Reflections in the y axis• Reflections can be made across the y-axis.
Check the corresponding points here.
Notice that the point (2, 1) corresponds to (-2, 1). The point (7, 1) corresponds to (-7, 1). The y
values stay the same, but the x values change sign.
In a reflection across the y axis, the point (x, y) reflects onto image (-x, y).
y-axis