Chapter 7's Top 10 Concepts

What is Isometry?

• Isometry is when an object remains the same after it has been transformed ((moved by a reflection, rotation or translation))

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• Reflection in the x-axis ------> ( x , y ) = ( x , -y)
• Reflection in the y-axis -------> ( x , y ) = ( -x , y)
• Reflection in the line y=x ------> ( x , y ) = ( y , x )
• Reflection in the origin ------> ( x , y ) = ( -x , -y )
• Rotation 90 degrees clockwise ((270 degrees counterclockwise)) about the origin ------> ( x , y ) = ( y , -x )
• Rotation 90 degrees counterclockwise ((270 degrees clockwise)) about the origin ------> ( x , y ) = ( -y , x )
• Rotation 180 degrees ((clockwise or counterclockwise)) about the origin ------> ( x , y ) = ( -x , -y ) ((same formula as a reflection in the origin!!!! ))
• Translation ------> ( x , y ) = ( x + a , y + b) ((if a =2, add 2 to the number
• Vector ------> < a , b >