Transformations and Symmetry Review

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape.

Front

What is translation in geometry?

Back

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

Front

How do you represent a translation mathematically?

Back

A translation can be represented as P: (x, y) → (x + a, y + b), where (a, b) is the vector of translation.

Front

What is reflection in geometry?

Back

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

Front

How do you find the image of a point after reflection over the y-axis?

Back

To find the image of a point (x, y) after reflection over the y-axis, the new coordinates will be (-x, y).

Front

What is the composition of transformations?

Back

The composition of transformations is the combination of two or more transformations applied one after the other.

Front

How do you denote the composition of two transformations T1 and T2?

Back

The composition of two transformations T1 and T2 is denoted as T1 ∘ T2.

Front

What is the effect of a reflection over the x-axis on a point (x, y)?

Back

The effect of a reflection over the x-axis on a point (x, y) is to change the coordinates to (x, -y).

Front

What is a vector in the context of translation?

Back

A vector in the context of translation is a quantity that has both direction and magnitude, indicating how far and in which direction to move a point.

Front

What does it mean to perform a transformation on a figure?

Back

Performing a transformation on a figure means applying a specific operation (like translation, reflection, or rotation) to change its position or orientation.