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.

Front

What are the four main types of transformations?

Back

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

Front

What is a translation?

Back

A translation moves every point of a shape the same distance in the same direction.

Front

How do you perform a 90° counterclockwise rotation about the origin?

Back

To rotate a point (x, y) 90° counterclockwise, the new coordinates will be (-y, x).

Front

How do you perform a 90° clockwise rotation about the origin?

Back

To rotate a point (x, y) 90° clockwise, the new coordinates will be (y, -x).

Front

What is a reflection in geometry?

Back

A reflection flips a shape over a line, creating a mirror image.

Front

What happens to the coordinates of a point reflected across the x-axis?

Back

The y-coordinate changes sign; if the point is (x, y), the reflected point is (x, -y).

Front

What happens to the coordinates of a point reflected across the y-axis?

Back

The x-coordinate changes sign; if the point is (x, y), the reflected point is (-x, y).

Front

What is the effect of reflecting a point across the line y = x?

Back

The x and y coordinates are swapped; if the point is (x, y), the reflected point is (y, x).

Front

What is the formula for translating a point (x, y) by (a, b)?

Back

The new coordinates after translation are (x + a, y + b).