translations, reflections, and rotations

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

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

Back

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

Front

What does it mean to reflect a point over the y-axis?

Back

To reflect a point (x, y) over the y-axis, the x-coordinate changes sign, resulting in the point (-x, y).

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

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

Back

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

Front

How do you reflect a point (3, 2) over the y-axis?

Back

The reflection is (-3, 2).

Front

What is the difference between a translation and a reflection?

Back

A translation moves a figure without changing its orientation, while a reflection flips a figure over a line, changing its orientation.

Front

What is the algebraic rule for translating a point (x, y) 2 units left and 9 units up?

Back

(x, y) --> (x - 2, y + 9)

Front

If triangle ABC is translated to triangle A'B'C', what does the notation A' represent?

Back

A' represents the image of point A after the translation.

Front

What is the effect of a 180° rotation on a point (x, y)?

Back

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