Unit 1: Transformations, Congruence, and Similarity.

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Presentation transcript:

Unit 1: Transformations, Congruence, and Similarity

Basic Types of Transformations: Translations Reflections Rotations

Quadrant I Quadrant II Quadrant III Quadrant IV x-axis y-axis (x,y)

Object to Image (Before) (After) Before Transformation:After Transformation: (‘ = PRIME) A A’ B B’ C C’

Translations…

A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction. Objects that are translated are congruent. *The word "translate" in Latin means "carried across".

Example 1: Translate the object down 2 and right 3 units.

Example 1 Solution: Translate the object down 2 and right 3 units.

Example 2: Translate the object (-3, 4)

Example 2 Solution: Translate the object (-3, 4)

Remember: Translations are SLIDING on a graph!!! The shape doesn’t change at all. Translations are SLIDES!!!

Reflections…

A reflection “flips” an object and can be seen in water, in a mirror, in glass, or in a shiny surface. An object and its reflection have the same shape and size, but the figures face in opposite directions. In a mirror, for example, right and left are switched.

The line (where a mirror may be placed) is called the line of reflection. The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection. A reflection can be thought of as a "flipping" of an object over the line of reflection. The object ABCD is being reflected over the x-axis.

Example 3: Reflect the object over the y-axis.

Example 3 Solution: Reflect the object over the y-axis.

Example 4: Reflect the object over x = 2.

Example 4 Solution: Reflect the object over x = 2.

Rotations…

A rotation is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation are the same shape and size, but the figures may be turned in different directions.

Rotations Graphically… Physically rotate the graph paper and use the original points – just graphed in the different quadrants.

Rules: When students complete rotating the original figure clockwise 90˚, 180˚, and 270˚, you can have them come up with the rules on their own. If you have time, you can have them use the same figure and rotate counter clockwise and come up with the rules of those too.

Rotation Rules: ClockwiseCounter Clockwise 90˚(y, -x)(-y, x) 180˚(-x, -y) 270˚(-y, x)(y, -x)

Rotate 90° counter clockwise

Rotate 90° clockwise