Geometric Transformations

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 translation, rotation, reflection, or dilation.

Front

Define translation in geometry.

Back

Translation is a transformation that moves every point of a shape the same distance in a specified direction.

Front

What is a rotation in geometry?

Back

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

Front

What does reflection mean in geometric transformations?

Back

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

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

How do you find the image of a point (x, y) after reflecting across the x-axis?

Back

The image of the point (x, y) after reflecting across the x-axis is (x, -y).

Front

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

Back

The coordinates change to (-x, y) when reflected across the y-axis.

Front

Describe the transformation that results from translating a point 5 units left and 1 unit up.

Back

The new coordinates of the point (x, y) will be (x - 5, y + 1).

Front

What is the result of a 180° rotation around the origin for a point (x, y)?

Back

The new coordinates after a 180° rotation are (-x, -y).

Front

Explain the sequence of transformations: Reflect across the x-axis and then rotate -90 degrees around the origin.

Back

First, reflect the shape over the x-axis, then rotate the resulting shape -90 degrees around the origin.