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Learn about the different types of transformations in geometry, including reflections, rotations, and translations. Practice identifying and drawing reflections. Homework: Bring in a picture that shows a reflection.
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DRILL • If A is in between points B and C and AC is 4x + 12 and AB is 3x – 4 and BC is 57 feet how long is AB? • Angles A and B are Supplementary if Angle A is 2x – 20 and Angle B is 4x – 44. Find the measure of Angle A.
Transformations • A transformation is any type of movement in geometry, it can be a change in shape, size, or simply location of an object. • The three types of Transformations we will talk about today are Reflections, Rotations and Translations.
Pre-Image And Image • Pre-Image is the original figure before any type of transformation takes place. • Image is the new figure after the transformation has taken place.
Vocabulary Isometry: a transformation in which the original figure and it’s image are congruent. Opposite Orientation: when an image appears to be backwards compared to the pre-image.
Reflection • A transformation in which a line of reflection acts as a mirror reflecting points from their pre-image to their image.
Reflections • A reflection reverses orientation. • A reflection is an isometry. • A reflection over the x-axis results in a change in the y-coordinate. • A reflection in the y-axis results in a change in the x-coordinate.
IS IT SYMMETRICAL? Directions • Take your paper, fold it so there are 4 sections. • Label each with Horizontal ONLY, Vertical ONLY, Both H &V, and/or Rotational
Which category does it fit? • Directions: Draw each picture under the correct type of symmetry.
An isometry is a transformation that does not change the shape or size of a figure. Reflections, translations, and rotations are all isometries. Isometries are also called congruence transformations or rigid motions. Recall that a reflection is a transformation that moves a figure (the preimage) by flipping it across a line. The reflected figure is called the image. A reflection is an isometry, so the image is always congruent to the preimage.
Patty Paper Reflection • Fold patty paper both ways, so that you have 4 boxes. Darken the folds and label the x and y axes. • Draw any TRIANGLE in the 2nd Quadrant
Reflection • Reflect your triangle over the x-axis. • What are the new coordinates?
Reflection • Reflect your original triangle over the y-axis • What are the new coordinates?
Reflection • Reflect your original over the line y=x. • What are the new coordinates?
Conclusion • What can we conclude about coordinates and reflections? • Over the X-axis? • Over the Y-axis? • Over the line y = x?
Rotational Symmetry • Wind Mill • How many degrees can each rotate?
Class work • Complete reflection in the coordinate plane handout
Wrap Up • Objective: SWBAT identify and draw reflections. • When asked to reflect this graph over the y-axis, this is the graph that was given. Is the student correct?
Complete Exit TicketHomework:Bring in a picture that shows a reflection.