Rigid motions Rigid Motion any way of moving

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Rigid motions Rigid Motion: any way of moving all the points in the plane

Rigid motions Rigid Motion: any way of moving all the points in the plane such that: a) the relative distance between points stays the same and b) the relative position of the points stays the same. There are four types of rigid motions that we will consider: translation , rotation, reflection, and glide reflection.

Translation: In a translation, everything is moved by the same amount and in the

Translation: In a translation, everything is moved by the same amount and in the same direction. Every translation has a direction and a distance.

Rotation: A rotation fixes one point (the rotocenter) and everything rotates by the same

Rotation: A rotation fixes one point (the rotocenter) and everything rotates by the same amount around that point. Every rotation has a rotocenter and an angle.

Reflection: A reflection fixes a mirror line in the plane and exchanges points from

Reflection: A reflection fixes a mirror line in the plane and exchanges points from one side of the line with points on the other side of the mirror at the same distance from the mirror. Every reflection has a mirror line.

Glide Reflection: A glide reflection is a mirror reflection followed by a translation parallel

Glide Reflection: A glide reflection is a mirror reflection followed by a translation parallel to the mirror. Every glide reflection has a mirror line and translation distance.

Translation Example 1. Example 2. Example 3.

Translation Example 1. Example 2. Example 3.

Class work

Class work

Solutions

Solutions

Write a rule to describe each transformations

Write a rule to describe each transformations

Solutions

Solutions

Reflections

Reflections

Repetition

Repetition

Example 1. Example 2. Kuta Software - Infinite Geometry for practice

Example 1. Example 2. Kuta Software - Infinite Geometry for practice

Find the coordinates of each image: Class work (1 -6) 1. Rx=2(A), A(2, 4)

Find the coordinates of each image: Class work (1 -6) 1. Rx=2(A), A(2, 4) 2. Rx=-2(B), B(-1, -3) 3. Ry=3(C), 4. Ry=-2(D), D(-4, 5) C(-2, 1) 5. Rx=1(∆ABC), A(1, 2), B(5, 2), C(3, 4) 6. Ry=1(∟ABC) (∟ABC =90 , B(x, y) is in the first quadrant, y ˃3 and x˃2 ). (extra credit) Home work (1 and 2) 1. Ry=-1(⌂ABCDE), A(1, 2), B(6, 2), C(5, 4), D(4, 5), E(2, 4) 2. Rx=2‹ABC (‹ABC is acute , B(x, y) is in the second quadrant, x˃-6 and y˂5 )

Class work

Class work

Solutions

Solutions

Class work

Class work

Solutions

Solutions

Home work (1 -12)

Home work (1 -12)

Look, remember and ask me if you have any doubts.

Look, remember and ask me if you have any doubts.