Section 7.3 Rigid Motion in a Plane Rotation

Bell Work 1.Using your notes, Reflect the figure in the y-axis. 2. Write all the coordinates for both the preimage and the image. P (, ) ⤍ P’(, ) Q (, ) ⤍ Q’(, ) R (, ) ⤍ R’(, ) S (, ) ⤍ S’(, ) S P R Q

Outcomes You will be able to identify what is a transformation and what is a rotation. You will be able to rotate a polygon on a coordinate grid about the origin.

Transformations A transformation is a change in the __size_, _location_, or _orientation_ of a figure. An Isometry is a transformation that preserves length, angle measures, parallel lines, and distances between points. Transformations that are isometries are called Rigid Motion Transformations. Isometry

Rotations Rotation - A Rotation is a transformation in which a figure is turned about a fixed point. The fixed point is called the center of rotation. Rays drawn from the center of rotation to a point and to its image form an angle called the angle of rotation. A Rotation is an Isometry.

Rotation- Turning about a fixed point How can we rotate (turn) objects? Clockwise (CW) Counter Clockwise (CCW)

Rotation For any rotation, we need to know the two D’s of rotations: 1)Degrees – how far 2)Direction – which way 180 degrees CCW

Rotations Example: T T T T H H H H 90 degrees CW 90 degrees CCW

Rotational Symmetry Symmetry? A figure has rotational symmetry if it can be mapped onto itself by rotation of 180° or less. For example, a square has rotational symmetry because it maps onto itself every 90° turn.

Example 2: Triangle ABC is labeled on your graph. Rotate Triangle ABC, 90 o counterclockwise about the origin. Label the triangle A′ B′ C′. Rotate Triangle ABC, 180 o counterclockwise about the origin. Label the triangle A″ B″ C″. Rotate Triangle ABC, 270 o counterclockwise about the origin. Label the triangle A′′′ B′′′ C′′′. Rotation Write coordinates of : A ( 1, 4 ) A’(, ) B( 5, 2 ) B’(, ) C( 2, 0 ) C’(, ) A’’ (, ) A’’’ (, ) B’’ (, ) B’’’ (, ) C’’ (, ) C’’’ (, )

Rotation Complete each rule for finding the image of any point (x, y) under the given rotation. a)90° rotation about the origin CCW: (x, y) → ( -y, x ) b)180° rotation about the origin CCW:(x, y) → ( -x, -y ) c)270° rotation about the origin CCW:(x, y) → ( y, -x ) d)360° rotation about the origin CCW:(x, y) → ( x, y )

Reflection 7a) Draw the final image created by rotating triangle RST 90° counterclockwise about the origin and then reflecting the image over the x-axis. (x, y) ⤍ ccw 90 (-y, x) ⤍ ref-x (x, -y) R( -4, 4) ⤍ R’(-4, -4) ⤍ R’’( -4, 4) S( -2, 3) ⤍ S’( -3, -2) ⤍ S”( -3, 2) T( -3, 1) ⤍ T’( -1, -3) ⤍ T’’( -1, 3)

Reflection 7.b) Draw the final image created by reflecting triangle RST in the x-axis and then rotating the image 90° counterclockwise about the origin. (x, y) ⤍ ref-x (x, -y) ⤍ ccw 90 (-y, x) R( -4, 4) ⤍ R’(-4, -4) ⤍ R’’( 4, -4) S( -2, 3) ⤍ S’( -2, -3) ⤍ S”( 3, -2) T( -3, 1) ⤍ T’( -3, -1) ⤍ T’’(1, -3) Are the final images in parts (a) and (b) the same? Why or why not?

Complete all practice problems Look over the IP and ask questions