Transformation Geometry

Front

What is Transformation Geometry?

Back

Transformation Geometry is a branch of geometry that deals with the movement of figures in a plane. It includes operations such as translation, rotation, reflection, and dilation.

Front

What is a translation in geometry?

Back

A translation is a type of transformation that moves every point of a figure the same distance in a specified direction.

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What does it mean to reflect a figure across a line?

Back

To reflect a figure across a line means to create a mirror image of the figure on the opposite side of the line.

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What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation, by a certain angle.

Front

What is the line of reflection for a figure reflected across the x-axis?

Back

The line of reflection is the x-axis itself, where each point (x, y) is transformed to (x, -y).

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

Back

To find the image of a point after a translation, add the translation vector to the original coordinates of the point.

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

Back

Reflecting a point (x, y) across the y-axis results in the point (-x, y).

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What is the effect of rotating a point 90 degrees counterclockwise around the origin?

Back

Rotating a point (x, y) 90 degrees counterclockwise around the origin results in the point (-y, x).

Front

What is the difference between a rigid transformation and a non-rigid transformation?

Back

A rigid transformation preserves the shape and size of a figure (e.g., translation, rotation, reflection), while a non-rigid transformation may change the size or shape (e.g., dilation).

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but maintains its shape, defined by a scale factor.