Transformations (Translations, Reflections, and Rotations)

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a shape a constant distance in a specified direction.

Front

What is the algebraic rule for translating a point (x, y) by 5 units right and 8 units down?

Back

(x, y) --> (x + 5, y - 8)

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a shape over a line, creating a mirror image.

Front

What is the algebraic rule for reflecting a point (x, y) over the x-axis?

Back

(x, y) --> (x, -y)

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a shape around a fixed point, called the center of rotation.

Front

What is the algebraic rule for rotating a point (x, y) 90 degrees clockwise around the origin?

Back

(x, y) --> (y, -x)

Front

What is the algebraic rule for rotating a point (x, y) 180 degrees around the origin?

Back

(x, y) --> (-x, -y)

Front

What is the algebraic rule for reflecting a point (x, y) over the y-axis?

Back

(x, y) --> (-x, y)

Front

If trapezoid ABCD is translated to trapezoid A'B'C'D' using the rule (x, y) --> (x + 5, y - 8), what happens to point A(2, 3)?

Back

Point A(2, 3) moves to A'(7, -5).

Front

What is the result of reflecting the point (6, -3) over the x-axis?

Back

(6, 3)