Translations on Coordinate Plane

Front

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

Back

A translation is a type of transformation that moves every point of a shape a certain distance in a specified direction without changing its size, shape, or orientation.

Front

How do you determine the new coordinates of a point after a translation?

Back

To find the new coordinates, add the translation values to the original coordinates. For example, if a point (x, y) is translated by (a, b), the new coordinates will be (x + a, y + b).

Front

What does a positive translation in the x-direction indicate?

Back

A positive translation in the x-direction means moving to the right on the coordinate plane.

Front

What does a negative translation in the y-direction indicate?

Back

A negative translation in the y-direction means moving down on the coordinate plane.

Front

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

Back

(8, 2) - The new coordinates are found by adding 5 to the x-coordinate and subtracting 2 from the y-coordinate.

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 left or right; only the y-coordinate may change.

Front

When translating a point, which coordinate is affected by a translation in the x-direction?

Back

The x-coordinate is affected by a translation in the x-direction.

Front

What is the translation rule for moving a point 4 units left and 3 units up?

Back

(x, y) → (x - 4, y + 3) - This rule indicates how to adjust the coordinates.

Front

If a triangle is translated 6 units to the right and 10 units up, how would you express this as a translation rule?

Back

(x, y) → (x + 6, y + 10) - This shows how to find the new coordinates after the translation.

Front

What happens to the coordinates of a point if it is translated 0 units in both directions?

Back

The coordinates remain unchanged; the point does not move.