Geometry Transformations

Front

What is a transformation in geometry?

Back

A transformation in geometry is an operation that moves or changes a shape in some way to produce a new shape. Common types of transformations include translations, rotations, reflections, and dilations.

Front

Define translation in geometry.

Back

Translation is a type of transformation that slides a shape in a straight line from one position to another without changing its size, shape, or orientation.

Front

What is the rule for translating a point (x, y) by (a, b)?

Back

The rule for translating a point (x, y) by (a, b) is given by (x + a, y + b).

Front

How do you rotate a point (x, y) 90 degrees counterclockwise around the origin?

Back

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

Front

What are the coordinates of point B' if point B(5, -1) is rotated 90 degrees counterclockwise around the origin?

Back

The coordinates of point B' will be (1, 5).

Front

Define reflection in geometry.

Back

Reflection is a transformation that flips a shape over a line, creating a mirror image of the original shape.

Front

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

Back

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

Front

What is the effect of reflecting a point across the line y=0?

Back

Reflecting a point across the line y=0 is the same as reflecting it across the x-axis.

Front

What is a rotation in geometry?

Back

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

Front

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

Back

To rotate a point (x, y) 180 degrees around the origin, the new coordinates will be (-x, -y).