Transformations

Front

What is a transformation in geometry?

Back

A transformation is a function that maps a set of points to another set of points, altering their position, size, or orientation.

Front

What are the four main types of transformations?

Back

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

Front

Define translation in geometry.

Back

Translation is a transformation that moves every point of a figure the same distance in the same direction.

Front

What is a rotation?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

Front

Explain reflection in geometry.

Back

Reflection is a transformation that flips a figure over a line, creating a mirror image.

Front

What is dilation?

Back

Dilation is a transformation that changes the size of a figure but not its shape, using a scale factor.

Front

How do you perform a translation of a point (x, y) by (a, b)?

Back

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

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 from (x, y) to (-x, y).

Front

If a point (x, y) is rotated 90 degrees counterclockwise around the origin, what are the new coordinates?

Back

The new coordinates will be (-y, x).

Front

What is the effect of a dilation with a scale factor of 2 on a point (x, y)?

Back

The new coordinates will be (2x, 2y), effectively doubling the distance from the origin.