Geometric Transformations

Front

What is a geometric transformation?

Back

A geometric transformation is an operation that moves or changes a shape in a specific way, including translations, rotations, reflections, and dilations.

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a shape around a fixed point, called the center of rotation, by a certain angle.

Front

What are the coordinates of a point after a 90-degree counterclockwise rotation?

Back

If a point (x, y) is rotated 90 degrees counterclockwise, its new coordinates will be (-y, x).

Front

What is the rule for a 270-degree clockwise rotation?

Back

The rule for a 270-degree clockwise rotation is (x, y) → (-y, x).

Front

What is dilation in geometry?

Back

Dilation is a transformation that changes the size of a shape but keeps its proportions the same, defined by a scale factor.

Front

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

Back

To find the image of a point (x, y) after dilation with a scale factor k, use the formula (kx, ky).

Front

What happens to the coordinates of a point when reflected over the x-axis?

Back

When a point (x, y) is reflected over the x-axis, its new coordinates become (x, -y).

Front

What happens to the coordinates of a point when reflected over the y-axis?

Back

When a point (x, y) is reflected over the y-axis, its new coordinates become (-x, y).

Front

What is the image of point T(4, -1) after a reflection over the line y = -x?

Back

The image of point T(4, -1) after reflection over the line y = -x is (1, -4).

Front

What is the scale factor in dilation?

Back

The scale factor in dilation is a number that determines how much the shape will be enlarged or reduced.