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 do you perform a translation on a point (x, y)?

Back

To translate a point (x, y) by (a, b), you add a to x and b to y, resulting in (x+a, y+b).

Front

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

Back

When a point (x, y) is reflected across the x-axis, its coordinates change to (x, -y).

Front

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

Back

When a point (x, y) is reflected across the y-axis, its coordinates change to (-x, y).

Front

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

Back

The coordinates change to (y, -x).

Front

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

Back

The coordinates change to (-y, x).

Front

How do you rotate a point (x, y) 180 degrees about the origin?

Back

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

Front

What is the effect of a dilation on a point (x, y) with a scale factor k?

Back

The coordinates change to (kx, ky), where k is the scale factor.

Front

If triangle ABC is translated by (x+3, y-2), what are the new coordinates of point A(1, 1)?

Back

The new coordinates of point A will be (1+3, 1-2) = (4, -1).