Geometry B: Translations

Front

What is a translation in geometry?

Back

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

Front

How do you describe a translation using coordinates?

Back

A translation can be described using the notation (x, y) -> (x + a, y + b), where 'a' is the horizontal shift and 'b' is the vertical shift.

Front

What does it mean to translate a shape 5 units right and 3 units up?

Back

It means to move the shape 5 units to the right along the x-axis and 3 units up along the y-axis.

Front

If a point A(2, 3) is translated 4 units left and 2 units down, what are the new coordinates?

Back

The new coordinates will be A'(-2, 1).

Front

What is the effect of translating a shape on its size and orientation?

Back

A translation does not change the size, shape, or orientation of the shape; it only changes its position.

Front

How do you find the coordinates of a translated triangle given its vertices?

Back

To find the coordinates of a translated triangle, apply the translation rule to each vertex of the triangle.

Front

What is the translation rule for moving a shape from (x, y) to (x - 1, y + 2)?

Back

This rule means to move the shape 1 unit left and 2 units up.

Front

If triangle ABC has vertices A(1, 2), B(3, 4), and C(5, 6), what are the vertices after a translation of (x, y) -> (x + 2, y - 3)?

Back

The new vertices will be A'(3, -1), B'(5, 1), and C'(7, 3).

Front

What is the difference between a translation and a reflection?

Back

A translation moves a shape without changing its orientation, while a reflection flips a shape over a line, changing its orientation.

Front

How can you represent a translation on a coordinate plane?

Back

A translation can be represented by drawing arrows from the original shape to its new position, indicating the direction and distance of the movement.