Transformation geometry

Front

What is transformation geometry?

Back

Transformation geometry is a branch of mathematics that studies the properties of figures that remain unchanged under certain operations, such as translations, rotations, reflections, and dilations.

Front

What are the four main types of transformations?

Back

The four main types of transformations are translation, rotation, reflection, and dilation.

Front

What is a rigid motion?

Back

A rigid motion is a transformation that preserves the size and shape of a figure, meaning the distances between points remain unchanged.

Front

Which transformation is NOT a rigid motion?

Back

Dilation is not a rigid motion because it changes the size of the figure.

Front

How does a translation affect a figure?

Back

A translation moves a figure from one location to another without changing its shape, size, or orientation.

Front

What is the rule for translating a point (x, y) 2 units to the right and 3 units up?

Back

The rule for this translation is (x + 2, y + 3).

Front

What happens to the coordinates of a point under a reflection over the x-axis?

Back

Under a reflection over the x-axis, the y-coordinate of the point changes sign, resulting in (x, -y).

Front

What is the effect of a dilation with a scale factor greater than 1?

Back

A dilation with a scale factor greater than 1 enlarges the figure, making it larger than the original.

Front

What is the effect of a dilation with a scale factor between 0 and 1?

Back

A dilation with a scale factor between 0 and 1 reduces the figure, making it smaller than the original.

Front

How do you find the image of a point B(-10, -6) under a dilation with center at the origin and scale factor k = 1/2?

Back

The image of point B under this dilation is (-5, -3).