Translation

Front

What is a translation in geometry?

Back

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

Front

How do you represent a translation algebraically?

Back

A translation can be represented as (x + a, y + b), where 'a' is the horizontal shift and 'b' is the vertical shift.

Front

What does the notation T_{(a, b)} represent?

Back

T_{(a, b)} represents a translation of 'a' units horizontally and 'b' units vertically.

Front

If a point (x, y) is translated by T_{(-3, 2)}, what are the new coordinates?

Back

The new coordinates will be (x - 3, y + 2).

Front

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

Back

Translation does not change the size or orientation of a shape; it only changes its position.

Front

How do you find the image of a point after translation?

Back

To find the image of a point after translation, add the translation vector to the original coordinates.

Front

What is the translation rule for moving a point from (2, 3) to (5, 7)?

Back

The translation rule is T_{(3, 4)}.

Front

If triangle ABC has vertices A(1, 2), B(3, 4), and C(5, 6), what are the coordinates after a translation T_{(2, -1)}?

Back

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

Front

What is the pre-image of a translated figure?

Back

The pre-image is the original figure before any transformations, such as translations, are applied.

Front

How do you determine the translation vector from one point to another?

Back

The translation vector can be determined by subtracting the coordinates of the original point from the coordinates of the new point.