Post on 26-Dec-2015
Algebra 1 Notes
Lesson 4-2:Transformations on the
Coordinate Plane
Mathematics Standards- Number, Number Sense and Operations: Demonstrate fluency in computations using real numbers.
- Geometry and Spatial Sense: Identify the reflection and rotation symmetries of two- and three-dimensional geometric figures.
- Geometry and Spatial Sense: Perform reflections and rotation using compass and straightedge constructions and dynamic geometry software.
Mathematics Standards-Geometry and Spatial Sense: Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane.
- Geometry and Spatial Sense: Show and describe the results of combinations of translations, reflections and rotations (compositions).
- Geometry and Spatial Sense: Analyze two-dimensional figures in a coordinate plane.
Vocabulary
• Transformation – Movement of figures
• Preimage –image before a transformation
• Image – Image after a transformation
Reflection
A figure is flipped over a line.
We will always flip figures over the x-axis or y-axis
Translation
A figure is slid in any direction.
To translate a point by an ordered pair (a, b), add a to the x-coordinate and b to the y-coordinate. You can also count on a graph.
Dilation
A figure is enlarged or reduced.
To dilate a figure by a scale factor k, multiply both coordinates by k.
If k > 1, the figure is enlarged.
If k < 1, the figure is reduced.
Rotation
A figure is turned around a point.
To rotate a figure 90º counterclockwise about the origin, switch the coordinates of each point and then multiply the new first coordinate by -1.
To rotate a figure 180º about the origin, multiply both coordinates of each point by -1.
Example 1
Identify each transformation.
a)
Example 1
Identify each transformation.
a) translation
b)
dilation
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