Transformation Geometry

Front

What is Transformation Geometry?

Back

Transformation Geometry is a branch of geometry that studies the properties of figures that remain unchanged under certain transformations such as translation, rotation, reflection, and dilation.

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in a specified direction, represented algebraically as (x + a, y + b).

Front

How do you perform a 180-degree rotation around the origin?

Back

To perform a 180-degree rotation around the origin, change the signs of both coordinates of the point (x, y) to get (-x, -y).

Front

What is the result of rotating the point (3, 4) 180 degrees around the origin?

Back

The result is (-3, -4).

Front

What is the rule for a 90-degree counterclockwise rotation around the origin?

Back

The rule is to transform the point (x, y) to (-y, x).

Front

What is the result of rotating the point (7, 8) 90 degrees counterclockwise around the origin?

Back

The result is (-8, 7).

Front

What is a reflection in geometry?

Back

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

Front

What is the rule for reflecting a point across the y-axis?

Back

To reflect a point (x, y) across the y-axis, change the sign of the x-coordinate to get (-x, y).

Front

What is the result of reflecting the point (5, -3) across the y-axis?

Back

The result is (-5, -3).

Front

What is the rule for reflecting a point across the line y = -1?

Back

To reflect a point (x, y) across the line y = -1, use the formula (x, -y - 2).