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, including translations, rotations, reflections, and dilations.

Front

What is a translation?

Back

A translation is a type of transformation that slides a shape from one position to another without turning it. It is defined by a vector that indicates the direction and distance of the slide.

Front

What is the rule for translating a point (x, y) 2 units left and 3 units up?

Back

(x, y) → (x - 2, y + 3)

Front

What happens to the coordinates of a point when it is reflected over the y-axis?

Back

When a point (x, y) is reflected over the y-axis, its coordinates change to (-x, y).

Front

What is the result of reflecting the point (-5, 2) over the y-axis?

Back

(5, 2)

Front

What are the three main types of transformations?

Back

The three main types of transformations are translations, reflections, and rotations.

Front

What is the rule for translating a point (x, y) 4 units right and 2 units down?

Back

(x, y) → (x + 4, y - 2)

Front

What does it mean for two shapes to be congruent?

Back

Two shapes are congruent if they have the same size and shape, meaning one can be transformed into the other through translations, rotations, or reflections.

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

What is the rule for rotating a point (x, y) 90 degrees counterclockwise around the origin?

Back

(x, y) → (-y, x)