Translations, Rotations and Reflections

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in a specified direction.

Front

How is a translation represented algebraically?

Back

A translation can be represented as (x, y) --> (x + a, y + b), where 'a' is the horizontal shift and 'b' is the vertical shift.

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

Front

How do you rotate a point (x, y) 90 degrees clockwise about the origin?

Back

The new coordinates will be (y, -x).

Front

What is a reflection in geometry?

Back

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

Front

How do you reflect a point (x, y) across the y-axis?

Back

The new coordinates will be (-x, y).

Front

What happens to the coordinates of a point when it is reflected across the x-axis?

Back

The new coordinates will be (x, -y).

Front

What is the effect of a translation of 5 units to the right on the point (3, 4)?

Back

The new coordinates will be (8, 4).

Front

What is the algebraic rule for a translation 3 units down?

Back

The rule is (x, y) --> (x, y - 3).

Front

If a triangle is rotated 180 degrees about the origin, what happens to the coordinates of point (x, y)?

Back

The new coordinates will be (-x, -y).