Translations

Front

What is a translation in geometry?

Back

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

Front

How do you represent a translation mathematically?

Back

A translation can be represented by a rule such as (x, y) → (x + a, y + b), where 'a' and 'b' are the distances moved in the x and y directions, respectively.

Front

What happens to the coordinates of a point when it is translated?

Back

The x-coordinate is adjusted by adding or subtracting a value, and the y-coordinate is adjusted similarly.

Front

If point P(2, 3) is translated using the rule (x, y) → (x + 4, y - 2), what are the new coordinates?

Back

P' = (6, 1)

Front

What does it mean to translate a shape on a coordinate plane?

Back

To translate a shape means to slide it to a new position without changing its size, shape, or orientation.

Front

What is the effect of translating a triangle on its vertices?

Back

The vertices of the triangle will move to new positions based on the translation rule applied.

Front

If a triangle has vertices A(1, 2), B(3, 4), and C(5, 6), and is translated by (x, y) → (x - 1, y + 3), what are the new vertices?

Back

A'(0, 5), B'(2, 7), C'(4, 9)

Front

What is the difference between a translation and a rotation?

Back

A translation slides a shape without changing its orientation, while a rotation turns a shape around a fixed point.

Front

When translating a point, what operations can be performed on the coordinates?

Back

You can add or subtract values from the x and y coordinates.

Front

If point Q(-1, 2) is translated using the rule (x, y) → (x + 3, y - 1), what are the coordinates of Q'?

Back

Q' = (2, 1)