Geometric Transformations Flashcard

Front

What is a geometric transformation?

Back

A geometric transformation is a function that moves or changes a shape in a specific way, such as rotation, translation, reflection, or dilation.

Front

Define rotation in geometry.

Back

Rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

Front

What is the effect of a 90° clockwise rotation on a point (x, y)?

Back

The new coordinates after a 90° clockwise rotation are (y, -x).

Front

What is translation in geometry?

Back

Translation is a transformation that slides a figure from one position to another without changing its shape, size, or orientation.

Front

How do you represent a translation mathematically?

Back

A translation can be represented as (x, y) → (x + a, y + b), where 'a' and 'b' are the horizontal and vertical shifts, respectively.

Front

Define reflection in geometry.

Back

Reflection is a transformation that flips a figure over a line, creating a mirror image.

Front

What happens to the coordinates of a point (x, y) when reflected over the x-axis?

Back

The new coordinates become (x, -y).

Front

What is dilation in geometry?

Back

Dilation is a transformation that changes the size of a figure but keeps its shape, defined by a scale factor.

Front

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

Back

To find the image of a point (x, y) after dilation with a scale factor 'k', multiply the coordinates by 'k': (kx, ky).

Front

What is the center of rotation?

Back

The center of rotation is the fixed point around which a figure is rotated.