Rotations

Rotation

Turn

all points of a figure a fixed point.

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To rotate a figure by hand you need: • a pencil • a straightedge • a compass • a protractor Is a rotation by hand a construction? Explain.

No. A protractor is used to measure angles. Since measurements are being used, this is not a construction.

Draw a Rotation

Example:

Rotate quadrilateral ABCD 45 ° counterclockwise about point X.

• Draw a segment from X to A.

• Measure a 45° angle with

as a side. Draw the other side.

• Use the compass to copy

onto the new ray. • Repeat this process for points B, C, and D.

• Connect points A', B', C', and D'.

Example:

Triangle LMN has vertices L(-2, -1), M(-1, 2), and N(1, -1). Draw the image of ∆ LMN under a rotation of 115 ° clockwise about the point Y(-4, -2).

Common Rotations about the Origin

To rotate a figure 90º counterclockwise, about the origin take each vertex and: 1. switch the coordinates 2. multiply the first coordinate (the new x) by -1 F(2, 2) G(4, 1.5) H(5, 4) F  (-2, 2) G  (-1.5, 4) H  (-4, 5)

Q(-3, 2) R(-3, 4) S(0, 5) T(0, 1) Q  (3, -2) R  (3, -4) S  (0, -4) T  (0, -1) To rotate a figure 180º, multiply both coordinates by -1.

Example

: Triangle XYZ has vertices X(-4, 1), Y(-1, 5), and Z(-6, 9). Find the coordinates of the vertices after a 90º counterclockwise rotation and graph the image.

Example

: Rectangle ABCD has vertices A(-1, 1), B(-5, 1), C(-5, 4), and D(-1, 4). Find the coordinates of the vertices after a 180º counterclockwise rotation and graph the image.

Rotational Symmetry

Turn the figure LESS THAN 360 ° so the image is the same as the pre-image.

Order

the number of rotations less than 360 ° (including 0 °)

Magnitude

the measure of each angle of rotation 360

order

5 72 °

9.3 Rotations 9.5 Dilations

Transcript 9.3 Rotations 9.5 Dilations