Translations, Rotations, Reflections, and Dilations.

Front

What is a translation in geometry?

Back

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

Front

How do you represent a translation mathematically?

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.

Front

What is the rule for rotating a point 180° about the origin?

Back

The rule is (x, y) → (-x, -y).

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 across the x-axis?

Back

To reflect a point (x, y) across the x-axis, the new point is (x, -y).

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape, using a scale factor.

Front

How do you represent a dilation mathematically?

Back

A dilation can be represented as (x, y) → (kx, ky), where 'k' is the scale factor.

Front

What is the difference between a translation and a rotation?

Back

A translation moves a figure without changing its orientation, while a rotation turns a figure around a point.

Front

What does it mean to slide a figure 3 units up and 2 units to the right?

Back

This is a translation represented as (x, y) → (x + 2, y + 3).