Transformations Flashcard Review

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 do you perform a translation of a point (x,y) by (a,b)?

Back

You add the values of a and b to the coordinates: (x,y) → (x+a, y+b).

Front

What is the result of translating the point (2, 3) by (3, -2)?

Back

The new point will be (2+3, 3-2) = (5, 1).

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation.

Front

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

Back

The rule is (x,y) → (-y, x).

Front

What is the rule for rotating a point (x,y) 180° about the origin?

Back

The rule is (x,y) → (-x, -y).

Front

What is the rule for rotating a point (x,y) 270° counterclockwise about the origin?

Back

The rule is (x,y) → (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

What is the line of reflection for a reflection across the y-axis?

Back

The line of reflection is the y-axis itself, where the x-coordinates of points change sign.

Front

What happens to the coordinates of a point (x,y) when reflected across the x-axis?

Back

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