Notes 48

Translations, Reflections, and Rotations

*Notes 48

VocabularyTransformation- changes the position or orientation of a figure. Image- the resulting figure after a transformation.Preimage- the original figure.Translation- figure slides along a straight line without

turning.Reflection- figure flips across a line of reflection,

creating a mirror image.Line of reflection- the line in which a figure flips

across to create a mirror image.Rotation- figure turns around a fixed point.

In mathematics, a transformationchanges the position or orientation of a figure. The resulting figure is the imageof the original figure, called the preimage. Images resulting from the transformations described in the next slides are congruent to the original figures.

TranslationThe figure slides along a straight line without turning.

Types of Transformations

ReflectionThe figure flips across a line of reflection, creating a mirror image.

Types of Transformations

RotationThe figure turns around a fixed point.

Types of Transformations

Identify each type of transformation.

Additional Example 1: Identifying Types of Transformations

The figure flips across the y-axis.

A. B.

It is a translation.It is a reflection.

The figure slides along a straight line.

Check It Out: Example 1Identify the type of transformation.

Additional Example 2: Graphing Transformations on a Coordinate Plane

Graph the translation of quadrilateral ABCD 4 units left and 2 units down.

Each vertex is moved 4 units left and 2 units down.

Additional Example 2 Continued

Write the coordinate of the vertices of the image.

The coordinates of the vertices of quadrilateral A'B'C'D' are A'(–3, 1), B'(0, 2), C'(0, –1), and D'(–3, –3).

Quadrilateral ABCD (x – 4, y – 2) A’B’C’D’A(1, 3) (1 – 4, 3 – 2) A’(–3, 1)B(4, 4) (4 – 4, 4 – 2) B’(0, 2)C(4, 1) (4 – 4, 1 – 2) C’(0, –1)D(1, –1) (1 – 4, –1 – 2) D’(–3, –3)

A’ is read “A prime” and is used to represent the point on the image that corresponds to point A of the original figure

Reading Math

Check It Out: Example 2Graph the translation of quadrilateral ABCD 5 units left and 3 units down.

Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image.

Additional Example 3: Graphing Reflections on a Coordinate Plane

A. x-axis

Additional Example 3 Continued

The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites.

The coordinates of the vertices of triangle A’D’C’ are A’(–3, –1), D’(0, 0), and C’(2, –2).

B. y-axis

Additional Example 3 Continued

The y-coordinates of the corresponding vertices are the same, and the x-coordinates of the corresponding vertices are opposites.

The coordinates of the vertices of triangle A’D’C’ are A’(3, 1), D’(0, 0), and C’(–2, 2).

Check It Out: Example 3Graph the reflection of quadrilateral ABCD across the x-axis.

Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° about the origin. Write the coordinates of the vertices of the image.

Additional Example 4: Graphing Rotations on a Coordinate Plane

x

y

A

B

C

3

–3

The corresponding sides, AC and AC’ make a 180° angle.

Notice that vertex C is 4 units to the right of vertex A, and vertex C’ is 4 units to the left of vertex A.

C’

B’

A’

The coordinates of the vertices of triangle A’B’C’ are A’(0, 0), B’(–2, –3), and C’(–4, 0).

Rotate the graph of quadrilateral ABCD 90° clockwise about the origin.

Check It Out: Example 4