Geometry Semester Review Topic 2

Front

What is a translation in geometry?

Back

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

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), add a to x and b to y, resulting in the new coordinates (x + a, y + b).

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation.

Front

How do you rotate a point 90° counterclockwise about the origin?

Back

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

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but keeps its shape, using a scale factor.

Front

How do you dilate a point (x, y) using a scale factor k?

Back

To dilate the point (x, y) using a scale factor k, multiply both coordinates by k, resulting in (kx, ky).

Front

What is a reflection in geometry?

Back

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

Front

How do you reflect a point (x, y) across the line x = a?

Back

To reflect the point (x, y) across the line x = a, the new coordinates will be (2a - x, y).

Front

What is the effect of a 180° rotation about the origin on a point (x, y)?

Back

A 180° rotation about the origin transforms the point (x, y) to (-x, -y).

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Back

The distance d between two points is given by the formula d = √((x2 - x1)² + (y2 - y1)²).