Transformations

Front

What is a transformation in geometry?

Back

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

Front

What are the four main types of transformations?

Back

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

Front

Describe a reflection transformation.

Back

A reflection transformation flips a shape over a line, creating a mirror image.

Front

What is the coordinate rule for a reflection over the line y = -x?

Back

The coordinate rule for a reflection over the line y = -x is (x, y) → (-y, -x).

Front

What is the effect of a 90-degree counter-clockwise rotation on the point (x, y)?

Back

The effect of a 90-degree counter-clockwise rotation on the point (x, y) is (x, y) → (-y, x).

Front

What is the equation of a parabola that opens downwards?

Back

The equation of a parabola that opens downwards can be expressed in the form y = -a(x - h)² + k, where (h, k) is the vertex.

Front

How do you determine the number of lines of symmetry in a figure?

Back

The number of lines of symmetry in a figure can be determined by identifying how many ways the figure can be folded to match itself.

Front

What is the coordinate rule for a rotation of 180 degrees about the origin?

Back

The coordinate rule for a rotation of 180 degrees about the origin is (x, y) → (-x, -y).

Front

What is the transformation rule for a translation of a point (x, y) by (a, b)?

Back

The transformation rule for a translation of a point (x, y) by (a, b) is (x, y) → (x + a, y + b).

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 shape, making it larger than the original.