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

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 find the scale factor in a dilation?

Back

The scale factor is found by dividing the distance from the center of dilation to a point on the image by the distance from the center of dilation to the corresponding point on the original figure.

Front

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

Back

When reflected over the x-axis, the coordinates change to (x, -y).

Front

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

Back

When reflected over the y-axis, the coordinates change to (-x, y).

Front

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

Back

The coordinates change to (-y, x).

Front

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

Back

The coordinates change to (-x, -y).

Front

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

Back

The coordinates change to (y, -x).

Front

If a triangle has vertices at (2, 3), (4, 5), and (6, 7), what are the new coordinates after a dilation with a scale factor of 2?

Back

The new coordinates will be (4, 6), (8, 10), and (12, 14).