Geometry Transformations

Front

What is a reflection in geometry?

Back

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

Front

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

Back

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

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in a specified direction.

Front

How do you translate a point (x, y) by (a, b)?

Back

To translate the point (x, y) by (a, b), add a to the x-coordinate and b to the y-coordinate: the image is (x+a, y+b).

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

Front

How do you rotate a point 180° about the origin?

Back

To rotate a point (x, y) 180° about the origin, change the signs of both coordinates: the image is (-x, -y).

Front

What is the line of reflection for the line y = x?

Back

The line of reflection y = x swaps the x and y coordinates of points: the image of (x, y) is (y, x).

Front

What is the effect of reflecting a point over the x-axis?

Back

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

Front

What is the effect of reflecting a point over the y-axis?

Back

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

Front

What is the coordinate of the image of point (3, 4) reflected over the line y = x?

Back

The image of (3, 4) reflected over the line y = x is (4, 3).