Transformations

Front

What is a transformation in geometry?

Back

A transformation is a function that maps a set of points in a plane to another set of points, altering their position, size, or orientation.

Front

Define translation in the context of transformations.

Back

Translation is a type of transformation that moves every point of a shape or object a constant distance in a specified direction.

Front

What are the coordinates of a point after translating it 3 units left and 9 units down from (1, 4)?

Back

(-2, -5)

Front

What is the effect of a rotation of 90 degrees counterclockwise on the point (x, y)?

Back

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

Front

If point A(2, 3) is translated to A'(5, 7), what is the translation vector?

Back

The translation vector is (3, 4).

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a shape over a line, creating a mirror image.

Front

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

Back

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

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a shape while maintaining its proportions, defined by a scale factor.

Front

If a shape is dilated by a scale factor of 2, what happens to its dimensions?

Back

All dimensions are multiplied by 2, making the shape twice as large.

Front

What is the difference between rotation and reflection?

Back

Rotation turns a shape around a point, while reflection flips it over a line.