Transformations Review

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape to create a new shape. Common types include translations, rotations, reflections, and dilations.

Front

What is dilation in geometry?

Back

Dilation is a transformation that changes the size of a figure but not its shape. It is defined by a scale factor and a center of dilation.

Front

What does a scale factor greater than 1 indicate in dilation?

Back

A scale factor greater than 1 indicates an enlargement of the figure.

Front

What does a scale factor less than 1 indicate in dilation?

Back

A scale factor less than 1 indicates a reduction of the figure.

Front

What is the rule for dilating a point (x, y) by a scale factor k?

Back

The rule for dilating a point (x, y) by a scale factor k is (x, y) → (kx, ky).

Front

How do you translate a point (x, y) by (a, b)?

Back

To translate a point (x, y) by (a, b), use the rule (x, y) → (x+a, y+b).

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 over the x-axis?

Back

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

Front

What is the effect of reflecting a point (x, y) over the y-axis?

Back

Reflecting a point (x, y) over the y-axis results in the point (-x, y).

Front

What is the effect of rotating a point (x, y) 90 degrees counterclockwise around the origin?

Back

Rotating a point (x, y) 90 degrees counterclockwise around the origin results in the point (-y, x).