Unit Activity: Introduction to Geometry and Transformations
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Transformations can be thought of as functions that take the points from one object (the pre-image) to the corresponding points
on another object (the image). In the unit, you saw examples of how algebra can be used to rewrite the coordinates of points after
they have been transformed. You can also use function notation to rewrite the coordinates. For example, these statements show
several different ways you can use function notation for the translation, T. of a point 6 units in the positive x direction:
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• T(x, y) = (x + 6,y)
• T:(x, y) = (x + 6,y)
• T<6,0>(x, y) = (x + 6,y)
• T6, O(x, y) = (x + 6,y)
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Part A
Write functions for each of the following transformations using function notation. Choose a different letter to represent each
function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in the counterclockwise
direction
• translation of a units to the right and bunits up
• reflection across the y-axis
• reflection across the x-axis
• rotation of 90 degrees counterclockwise about the origin, point
• rotation of 180 degrees counterclockwise about the origin, point o
• rotation of 270 degrees counterclockwise about the origin, point o
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