Geometric Transformations REVIEW

Front

What is a geometric transformation?

Back

A geometric transformation is an operation 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 figure the same distance in a specified direction.

Front

What is the rule for translating a point (x, y) by a vector ⟨a, b⟩?

Back

The rule is (x, y) → (x + a, y + b).

Front

What does it mean to reflect a figure over the x-axis?

Back

Reflecting a figure over the x-axis means to flip it over the x-axis, changing the sign of the y-coordinates.

Front

What is the effect of rotating a figure 90° clockwise about the origin?

Back

The effect is that the coordinates of a point (x, y) change to (y, -x).

Front

What is dilation in geometry?

Back

Dilation is a transformation that changes the size of a figure but not its shape, using a scale factor.

Front

What is the rule for dilating a point (x, y) by a scale factor of k?

Back

The rule is (x, y) → (kx, ky).

Front

How do you describe a reflection over the y-axis?

Back

A reflection over the y-axis changes the sign of the x-coordinates of the points in the figure.

Front

What is the vector representation of a translation 3 units right and 2 units up?

Back

The vector representation is ⟨3, 2⟩.

Front

What is the result of reflecting a point (x, y) over the line y = x?

Back

The result is (y, x).