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.

Front

What are the four main types of transformations?

Back

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

Front

What does it mean to translate a point in the coordinate plane?

Back

To translate a point means to move it a certain distance in a specified direction without changing its shape or orientation.

Front

How do you reflect a point over the x-axis?

Back

To reflect a point (x, y) over the x-axis, the new point will be (x, -y).

Front

How do you reflect a point over the y-axis?

Back

To reflect a point (x, y) over the y-axis, the new point will be (-x, y).

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.

Front

What is the result of rotating a point 90 degrees counterclockwise about the origin?

Back

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

Front

What happens to the coordinates of a point when it is rotated 180 degrees about the origin?

Back

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

Front

What is the effect of a dilation on a shape?

Back

A dilation changes the size of a shape but keeps its proportions the same.

Front

What is the rule for translating a point (x, y) 4 units left?

Back

The new coordinates will be (x - 4, y).