CC GPS Coordinate Algebra Unit 5 – Transformations in the Coordinate Plane
Name______Review #2 3/26/14
Write the rule for each transformation.
1. Reflection over the x-axis 2. Reflection over the y-axis
3. Reflection over the line y = x 4. Reflection over the line y = -x
5. 90 degree rotation clockwise 6. 90 degree rotation counterclockwise
7. 180 degree rotation
Use the given rule to find A’. State what type of transformation is taking place. (Translation, Reflection, Rotation, Dilation, Horizontal Stretch/Shrink, or Vertical Stretch/Shrink)
8. (x, y) →(x + 4, y – 7) A( -3, -8) A’ ______Type ______
9. (x, y) →(-x,- y) A(8, 5) A’ ______Type ______
10. (x, y)→(-x, y) A(-3, 4) A’ ______Type ______
11. (x, y)→(-y, -x) A(-12, 1) A’ ______Type ______
12. (x, y) →(y, -x) A(4, 1) A’ ______Type ______
13. How many degrees would you have to turn the hexagon clockwise to
get piece #2 in the bottom center position (where #1 started)?
State which type of transformation takes place in the graph. BE SPECIFIC.
14. 15.
16. Use the graph to the right to answer questions a – c. BE SPECIFIC
a) What transformation takes ∆ABC to ∆A’B’C’?
b) What transformation takes ∆ A’B’C’ to ∆A”B”C”?
c) What single transformation could have been done
to go directly from ∆ABC to ∆A”B”C”?
17. Use the graph to the right to answer questions a – c. BE SPECIFIC
a) What transformation takes quadrilateral MNOP to M’N’O’P?
b) What transformation takes quadrilateral M’N’O’P’ to
M”N”O”P”?
c) What single transformation could have been done
to go directly from quadrilateral MNOP to M”N”O”P”?
Perform the transformations. LABEL.
18. Translation (x, y) à (x + 8, y – 3) 19. Reflection across the line y = x.
20. Translate MNOP (x,y) ->(x -6, y-3) followed by 21. Translation using the rule(x,y)--> (x+3, y)
a reflection over the line x = 2. followed by a rotation of 180 degrees around the origin.
List all coordinates:
P( ) ->P’( )-> P’’( ) O( )-> O’ ( )-> O’’( )
M( )-> M’( )->M’’( ) N( )-> N’( ) ->N’’( )
22. Glide reflection- translate JKL 5 units 23. Rotation 90° clockwise about the origin followed
to the left followed by a by a reflection across the y-axis.
reflection of the line y = -2
24. Which one of the images can be rotated to match the letter J on the left?
(a) (b) (c)
25. Which one of the images can be reflected to match the letter Z on the left?
(a) (b) (c)
How many lines of symmetry does the given object appear to have?
26. 27.
28. In the diagram, and DABC is reflected first in line
and then in line m. This set of reflections is equivalent to
doing what kind of singular transformation?
29. If and m were intersecting lines, and DABC was reflected first in line and then in line m, what would the resulting transformation be?
Describe any rotations (of 180° or less) that will map each figure onto itself.
30. 31. 32.
An isometry is a transformation in the plane that preserves length. Identify each transformation that is an isometry. For the ones that are isometries, identify which type of transformation is shown. (Preimages are unshaded and images are shaded.)
33. 34. 35. 36. 37.
Multiple Transformations: Label each step correctly.
38. Translation (x, y) à (x + 9, y – 8) 39. Translation (x, y) à (x + 4, y – 2)
Rotation 90° CCW about the origin Rotation 180° about the origin.
Reflection about the line y = x.
40. State the degree of rotation for each figure that is less than or equal to 1800.