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

Define translation in geometry.

Back

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

Front

What does it mean to reflect a shape over the x-axis?

Back

Reflecting a shape over the x-axis means to flip it over the x-axis, changing the sign of the y-coordinates of the points.

Front

How do you reflect a point (x, y) over the y-axis?

Back

To reflect a point (x, y) over the y-axis, change the sign of the x-coordinate: the new point is (-x, y).

Front

What is the result of translating the point (3, 2) 4 units to the right?

Back

The new point will be (7, 2).

Front

What is the rule for a translation of 5 units down?

Back

The rule is (x, y) → (x, y - 5).

Front

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

Back

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

Front

What happens to the coordinates of a point when it is reflected over the line y = x?

Back

The coordinates switch places: (x, y) becomes (y, x).

Front

Define dilation in geometry.

Back

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