Translations

Front

What is a translation in geometry?

Back

A translation is a type of 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

If a point (3, 4) is translated 5 units to the right and 2 units down, what is the new position?

Back

(8, 2) - The point moves right by 5 (3 + 5) and down by 2 (4 - 2).

Front

What does the term 'pre-image' refer to in transformations?

Back

The pre-image is the original figure before any transformation is applied.

Front

What does the term 'image' refer to in transformations?

Back

The image is the resulting figure after a transformation has been applied.

Front

Which axis is the vertical (up-down) one?

Back

y-axis.

Front

What is the effect of translating a figure 10 units left?

Back

The x-coordinates of all points in the figure decrease by 10.

Front

If a triangle is translated according to the rule (x-3, y+4), what happens to its coordinates?

Back

Each x-coordinate decreases by 3 and each y-coordinate increases by 4.

Front

What is the algebraic notation for a figure translated 4 units left and 3 units down?

Back

(x, y) --> (x - 4, y - 3).

Front

How do you determine the direction of a translation?

Back

The direction is determined by the signs of the values added to the x and y coordinates: positive for right/up and negative for left/down.