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

Define translation in the context of transformations.

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 does the rule (x,y) → (y,-x) represent?

Back

This rule represents a rotation of 90 degrees counterclockwise around the origin.

Front

How do you perform a reflection across the y-axis?

Back

To reflect a point (x,y) across 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 (3,4) 2 units left and 1 unit down?

Back

The new point is (1,3).

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

Identify the transformation: (x,y) → (x+5, y-2).

Back

This represents a translation 5 units to the right and 2 units down.

Front

What is the effect of a reflection across the x-axis on the point (4,-3)?

Back

The new point after reflection is (4,3).

Front

If point A(2,3) is reflected across the line y=x, what is the new location of point A?

Back

The new location of point A is (3,2).

Front

What does the transformation (x,y) → (x-2, y+3) do to a point?

Back

This transformation translates the point 2 units left and 3 units up.