Translations on Coordinate Plane

Front

What is a translation in the context of the coordinate plane?

Back

A translation is a transformation that moves every point of a shape or object a constant distance in a specified direction.

Front

How do you represent a translation mathematically?

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 a positive value for 'a' indicate in a translation?

Back

A positive value for 'a' indicates a translation to the right on the x-axis.

Front

What does a negative value for 'b' indicate in a translation?

Back

A negative value for 'b' indicates a translation downward on the y-axis.

Front

If a point (3, 4) is translated by the vector (2, -5), what are the new coordinates?

Back

The new coordinates are (5, -1).

Front

What is the effect of translating a shape 0 units in the x-direction?

Back

Translating a shape 0 units in the x-direction means it will not move horizontally.

Front

How do you find the new coordinates after a translation?

Back

To find the new coordinates, add the translation vector to the original coordinates: (x, y) + (a, b) = (x + a, y + b).

Front

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

Back

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

Front

If a triangle is translated 6 units to the right and 2 units down, what is the translation vector?

Back

The translation vector is (6, -2).

Front

How can you determine the direction of a translation on a coordinate plane?

Back

The direction of a translation can be determined by the signs of the values in the translation vector: positive for right/up and negative for left/down.