9-3 Rotations

You identified rotations and verified them as congruence transformations.

• Draw rotations.

• Draw rotations in the coordinate plane.

How Many Degrees…

…are in a half turn?

…are in a quarter turn?

…three quarters turn?

180°

90°

270°

DefinitionA rotation is a transformation that turns a set of

points about one point, the center of rotation. The pre-image and image of any point are the same distance from the center of rotation.

Q

P (Pre-image)

P’ (Image)Center of rotation

Angle of rotation45°

Definition continuedThe angle of rotation measures how much a point

is turned about the center. For example, if point P is rotated 45° clockwise about center of rotation Q, 45'PQPm

Q

P (Pre-image)

P’ (Image)Center of rotation

Angle of rotation45°

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Draw a RotationRotate quadrilateral RSTV 45° counterclockwise about point A.

• Use a protractor to measure a 45° angle counterclockwise with as one side. Extend the other side to be longer than AR.

• Draw a segment from point R to point A.

• Locate point R' so that AR = AR'.• Repeat this process for points S,

T, and V.• Connect the four points to form

R'S'T'V'.Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A.

Answer:

A. 20° clockwiseB. 20° counterclockwiseC. 90° clockwiseD. 90° counterclockwise

For the diagram, which description best identifies the rotation of triangle ABC around point Q?

When a point is rotated 90°, 180°, or 270° counterclockwise around (0,0), you can use these rules:

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Spin ItWhen will the image

exactly overlap the pre-image?

30° clockwise60°clockwise90°clockwise120°clockwise

If a figure can be rotated onto itself with an angle or rotation between 0° and 360 °, the figure has rotational symmetry.

Rotations in the Coordinate PlaneTriangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Graph ΔDEF and its image after a rotation of 115° clockwise about the point G(–4, –2).First, draw ΔDEF and plot point G.

Use a protractor to measure a 115° angle clockwise with as one side.

Use a compass to copy onto Name the segment

Draw

Repeat with points E and F.

Draw a segment from point G to point D.

ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G.

Answer:

Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6). Draw the image of ΔABC under a rotation of 70° counterclockwise about the point M(–1, –1).A. B.

C. D.

9-3 ASSIGNMENT

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