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| |
|What you need to know|Things to remember |Problem |Problem |
|& be able to do | | | |
|Translations |Find the new coordinates by adding/ |Translate the following points by the rule: |Translation: (x, y) ( (x – 2, y – 6) |
| |subtracting the given value. |[pic] |W(3, 2) C(2, 4) T(3, 5) Z(5,2) |
| |Find the pre-image by doing the | | |
| |OPPOSITE. | | |
| | |S (-5, 2)( | |
| | |Y (-4, 5)( | |
| | |R (-1, 1)( | |
| | |A (-4, -2)( | |
|Reflections |Reflection over x-axis: (x, -y) |Reflection over y = x |Reflection over y = -3 |
| |Reflection over y-axis: (-x, y) | | |
| |Reflection over y=x: (y, x) | | |
| |Reflections over y= -x: (-y, -x) | | |
| |Reflection over any other line: PROTECT| | |
| |THE DISTANCE | | |
|Rotations |90CW/270CCW: (y, -x) |Rotate the figure 90 CW |Rotate the figure 90 CCW |
| |180: (-x, -y) | | |
| |90CCW/270CW: (-y, x) | | |
|Even, Odd or Neither |Even = Reflection over y-axis OR all |[pic] | [pic] |
| |even exponents (don’t forget constants)| | |
| | | | |
| |Odd = 180 Rotation OR all odd exponents| | |
| |(don’t forget x) | | |
| | | | |
Translation Practice
|1.Translate the image by (x + 4, y – 6) |2.Translate the image by (3x – 1, y + 5) |
| | |
|[pic] |[pic] |
|3.Find the pre-image (x – 9, y + 13) |4.Find the pre-image (x + 7, y – 19) |
| | |
|[pic] |[pic] |
| 5. Translate the image. | 6. Translate the image. |
|[pic] |[pic] |
| 8. Translate the image. | 9. Translate the image. |
|[pic] |[pic] |
|10. Write a rule for the given translation. |11. Write a rule for the given translation. |
|Translation : ∆XJZ to ∆[pic] |Translation ∆XJZ to ∆[pic] |
|[pic] |[pic] |
|13. Write a rule for the given translation. |14. Write a rule for the given translation. |
|Translation : Poly FYDI to Poly [pic] |Translation : Poly PIWK to Poly [pic] |
|[pic] |[pic] |
| | |
Practice problems on Reflection
Find the coordinates of the vertices of each figure after the given transformation.
1. Reflection across the x-axis.
[pic]
1. Reflect across the y-axis.
[pic]
[pic]
2. Reflect across the line y = x.
[pic]
3. Reflect across the line y = -x.
[pic]
[pic]
4. Reflect across the y-axis.
[pic]
5. Reflect across the line y = -x.
[pic]
[pic]
6. Reflect across the x-axis.
[pic]
7. Reflect across the line y = x.
[pic]
[pic]
[pic]
8. Reflect the image across the y-axis.
[pic]
9. Reflect the image across the x-axis.
[pic]
[pic]
10. Reflect the image across the y-axis.
[pic]
11. Reflect the image across the x-axis.
[pic]
[pic]
Write a rule to describe each transformation.
12. [pic]
13. [pic]
[pic]
14. [pic]
15. [pic]
Rotations Practice
[pic]
1. Where will the L-Shape be if it is…
a. rotated 180° around the origin? b. rotated 90° clockwise around the origin?
c. rotated 90° counterclockwise around the origin? d. rotated 270° clockwise around the origin?
e. rotated 90° counterclockwise around the point (3, 0)?
2. Rotate each figure about the origin using the given clockwise angle.
a. 180° b. 270° c. 90°
[pic] [pic] [pic]
d. 270° e. 180° f. 90°
[pic] [pic] [pic]
3. Find the angle of rotation for the graphs below. The center of rotation is the origin, and the darker image is the preimage. Your answer will be 90°, 270°, or 180° counterclockwise.
a. b. c.
[pic] [pic] [pic]
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[pic]
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