Translations and Reflections

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a shape a constant distance in a specified direction.

Front

How do you perform a translation on a point (x, y) by (a, b)?

Back

To translate the point (x, y) by (a, b), you add a to x and b to y, resulting in the new point (x+a, y+b).

Front

What is the result of translating the point (2, 3) by (3, -2)?

Back

The new point after translation is (2+3, 3-2) = (5, 1).

Front

What does it mean to reflect a shape across the y-axis?

Back

Reflecting a shape across the y-axis means that each point (x, y) of the shape is transformed to (-x, y).

Front

What is the result of reflecting the point (4, 5) across the y-axis?

Back

The new point after reflection is (-4, 5).

Front

What does it mean to reflect a shape across the x-axis?

Back

Reflecting a shape across the x-axis means that each point (x, y) of the shape is transformed to (x, -y).

Front

What is the result of reflecting the point (3, -2) across the x-axis?

Back

The new point after reflection is (3, 2).

Front

If a shape is translated 5 units down and 4 units to the right, what is the translation vector?

Back

The translation vector is (4, -5).

Front

How do you determine the new position of a shape after a translation?

Back

You apply the translation vector to each vertex of the shape by adding the vector's components to the coordinates of the vertices.

Front

What is the effect of translating a shape 3 units left and 3 units down?

Back

The shape moves to the left and downward, changing each point (x, y) to (x-3, y-3).