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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