Translations, Rotations, Reflections, and Dilations.

Front

What is a translation in geometry?

Back

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

Front

What is a rotation in geometry?

Back

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

Front

What is a reflection in geometry?

Back

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

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a shape by a scale factor, while maintaining its shape.

Front

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

Back

To translate the point (x, y) by (a, b), add a to x and b to y: (x + a, y + b).

Front

What is the scale factor in a dilation?

Back

The scale factor is the ratio of the distance from the center of dilation to a point on the image to the distance from the center of dilation to the corresponding point on the original shape.

Front

If a triangle is reflected over the x-axis, what happens to its coordinates?

Back

The y-coordinates of the triangle's vertices change sign, while the x-coordinates remain the same.

Front

What is the effect of a 90-degree rotation counterclockwise on the point (x, y)?

Back

The new coordinates after a 90-degree counterclockwise rotation are (-y, x).

Front

What is the effect of a dilation with a scale factor of 2 on the point (3, 4)?

Back

The new coordinates after dilation are (6, 8).

Front

How do you identify a reflection in a graph?

Back

A reflection can be identified by looking for symmetry across a line, where each point on one side of the line has a corresponding point on the opposite side at the same distance.