Transformations

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 perform a translation of a point (x, y) by (a, b)?

Back

To translate the point (x, y) by (a, b), you add a to the x-coordinate and b to the y-coordinate, resulting in the new point (x + a, y + b).

Front

What is the effect of reflecting a point over the y-axis?

Back

Reflecting a point (x, y) over the y-axis changes the x-coordinate to its opposite, resulting in the point (-x, y).

Front

What happens to the coordinates of a point when it is rotated 90 degrees counterclockwise about the origin?

Back

When a point (x, y) is rotated 90 degrees counterclockwise about the origin, its new coordinates become (-y, x).

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but may differ in size, meaning their corresponding angles are congruent and their corresponding sides are in proportion.

Front

What is a scale factor in geometry?

Back

A scale factor is a number that scales, or multiplies, some quantity. In the context of similar figures, it is the ratio of the lengths of corresponding sides.

Front

If a figure is enlarged by a scale factor of 3, what happens to its dimensions?

Back

If a figure is enlarged by a scale factor of 3, each dimension of the figure is multiplied by 3, resulting in a figure that is three times larger in each direction.

Front

What is the relationship between the angles of similar figures?

Back

All corresponding angles in similar figures are congruent.

Front

How do you find the image of a point after a transformation?

Back

To find the image of a point after a transformation, apply the specific rules of the transformation (translation, reflection, rotation, etc.) to the original coordinates.

Front

What is the formula for a reflection over the x-axis?

Back

Reflecting a point (x, y) over the x-axis changes the y-coordinate to its opposite, resulting in the point (x, -y).