Transformations TRANSLATION REFLECTION Objective Recognize lines of symmetry

Transformations TRANSLATION REFLECTION

Objective: • Recognize lines of symmetry and points of symmetry. • Draw a reflected image using coordinates. Sec 9. 1

4 Types of Transformations 1. Reflections: Flip 2. Translations: Slide 3. Rotations: Turn 4. Dilations: shrink or enlarge

Reflection: � Symmetry

Reflection over the x-axis � Two points are symmetric with respect to the x-axis if they have the same x-coordinate but opposite y-coordinate. For example: a) b) c) d)

Reflections over the y-axis � Two points are symmetric with respect to the y-axis if they have the opposite x-coordinate but same y-coordinate. For example: a) b) c) d)

Reflection Through the origin � Two points are symmetric with respect to the origin if both their x and y coordinates are opposites. For example: a) b) c) d)

Reflection over the line y= x �

Reflections Cheat Sheet �

Reflection across the x-axis Example 1: Preimage x Y W -5 4 X -1 4 Y 0 2 V -4 1 Image x y

Reflection across the y-axis Example 2: Preimage x y W 2 5 X 5 4 Y 3 2 V 2 3 Image x y

Example 3: Preimage x y R -4 1 S -2 0 Q -5 -4 Image x y

Reflection through the origin Example 4: Preimage x y K -4 4 L -1 1 J -3 -1 Image x y

Reflection over the x-axis Example 6: Preimage x y -1 -4 -3 -1 -2 -1 1 -2 Image x y

Reflection over the y-axis Example 7: Preimage x y -5 0 -5 5 -2 5 -3 0 Image x y

Example 8: Preimage x y 2 4 2 5 4 1 Image x y

Reflection through the origin Example 9: Preimage x y -1 -4 -3 -1 -2 -1 1 -2 Image x y

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