Translations, Reflections & Rotations

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a shape or object a certain distance in a specified direction without changing its size, shape, or orientation.

Front

When translating left or right on a coordinate plane, which coordinate is affected?

Back

x-coordinate

Front

What is a reflection in geometry?

Back

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

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 to get (-x, y).

Front

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

Back

When a point (x, y) is reflected over the x-axis, the y-coordinate changes sign, resulting in (x, -y).

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 are the coordinates of a point after a 90º counterclockwise rotation about the origin?

Back

If a point (x, y) is rotated 90º counterclockwise about the origin, its new coordinates will be (-y, x).

Front

If Triangle XYZ has vertices X(-9, 7), Y(-3, 5), and Z(-1, 12, what are the new coordinates of X' after a translation of 3 units left and 1 unit up?

Back

(-12, 8) because you subtract 3 from the x-coordinate and add 1 to the y-coordinate.

Front

What is the effect of a translation of 5 units up on the point (2, 3)?

Back

The new coordinates will be (2, 8) because you add 5 to the y-coordinate.

Front

How do you find the image of a point after a reflection over the y-axis?

Back

To find the image of a point (x, y) after reflection over the y-axis, the new coordinates will be (-x, y).