9-3 rotations
DESCRIPTION
9-3 Rotations. You identified rotations and verified them as congruence transformations. . Draw rotations. Draw rotations in the coordinate plane. How Many Degrees…. 180 ° 90° 270°. …are in a half turn? …are in a quarter turn? …three quarters turn?. Definition. - PowerPoint PPT PresentationTRANSCRIPT
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°
p. 640
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:
p. 641
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
PAGE 643, 6-10 EVEN, 11-13, 14-18