translations

Front

What is a translation in geometry?

Back

A translation is a 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, 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 2 units down?

Back

It means to move the shape 5 units in the positive x-direction and 2 units in the negative y-direction.

Front

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

Back

The new coordinates are (1, 7).

Front

What is the effect of translating a shape 0 units horizontally and 5 units vertically?

Back

The shape will move straight up by 5 units without any horizontal movement.

Front

How do you translate a triangle with vertices A(1, 2), B(3, 4), and C(5, 6) by (x - 2, y + 3)?

Back

The new vertices will be A(-1, 5), B(1, 7), and C(3, 9).

Front

What is the translation vector for moving a shape 4 units down and 3 units left?

Back

The translation vector is (-3, -4).

Front

If a shape is translated using the rule (x, y) → (x + 5, y - 2), what is the direction of the translation?

Back

The shape is translated 5 units to the right and 2 units down.

Front

What happens to the coordinates of a point when it is translated 7 units up?

Back

The y-coordinate of the point increases by 7.

Front

How do you find the translation needed to move point (2, 3) to point (5, 1)?

Back

The translation is (5 - 2, 1 - 3) = (3, -2).