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 figure 5 units down and 3 units to the right?

Back

It means to move every point of the figure 5 units down on the y-axis and 3 units to the right on the x-axis.

Front

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

Back

The new position is (-2, 5).

Front

What is the effect of translating a triangle 2 units up?

Back

Each vertex of the triangle will move 2 units higher on the y-axis.

Front

How do you find the translation vector for moving from point A(1, 2) to point B(4, 5)?

Back

The translation vector is (4 - 1, 5 - 2) = (3, 3).

Front

What is the result of translating the point (x, y) by (3, -2)?

Back

The result is (x + 3, y - 2).

Front

If triangle A'B'C' is translated to triangle ABC, what does this imply about their positions?

Back

It implies that triangle ABC is the image of triangle A'B'C' after a specific translation.

Front

What is the translation of a figure represented by (x, y) → (x + 9, y - 3)?

Back

This represents a translation 9 units to the right and 3 units down.

Front

How can you determine the direction of a translation?

Back

By analyzing the changes in the x and y coordinates of the points before and after the translation.