Unit 3A – CP CFA: Transformations

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape, called the image.

Front

What are the four main types of transformations?

Back

The four main types of transformations are translation, rotation, reflection, and dilation.

Front

How does a translation affect the coordinates of a point?

Back

A translation moves a point a certain distance in a specified direction, changing its coordinates according to the rule (x, y) -> (x + a, y + b), where a and b are the distances moved in the x and y directions respectively.

Front

What happens to the coordinates of a point when it is rotated 180° about the origin?

Back

The coordinates of a point (x, y) become (-x, -y) after a 180° rotation about the origin.

Front

What is the algebraic rule for translating a point 5 units to the right and 8 units down?

Back

The algebraic rule is (x, y) -> (x + 5, y - 8).

Front

How do you reflect a point across the y-axis?

Back

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

Front

What is the result of reflecting a point across the line x = -2?

Back

To reflect a point (x, y) across the line x = -2, the new x-coordinate is calculated as -2 - (x + 2), resulting in the new coordinates (-4 - x, y).

Front

What is the effect of a 270° counterclockwise rotation on a point (x, y)?

Back

The coordinates of the point (x, y) become (y, -x) after a 270° counterclockwise rotation.

Front

What does it mean to translate a point 2 units to the right and 8 units down?

Back

It means to add 2 to the x-coordinate and subtract 8 from the y-coordinate of the point.

Front

How do you describe a reflection across the line y = -2?

Back

To reflect a point (x, y) across the line y = -2, the new y-coordinate is calculated as -2 - (y + 2), resulting in the new coordinates (x, -4 - y).