Flashcard 3 - Transformations

Front

What are transformations in geometry?

Back

Transformations are operations that alter the position, size, or shape of a figure in the coordinate plane. Common types include translations, rotations, reflections, and dilations.

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a figure over a line, creating a mirror image. For example, reflecting a point (x, y) over the y-axis results in (-x, y).

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation, by a certain angle. For example, rotating a point (x, y) 90 degrees clockwise results in (y, -x).

Front

What is a translation in geometry?

Back

A translation is a transformation that slides a figure from one position to another without changing its shape or orientation. For example, translating a point (x, y) by (a, b) results in (x+a, y+b).

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure while maintaining its shape. It is defined by a scale factor, which determines how much the figure is enlarged or reduced.

Front

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

Back

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

Front

How do you find the coordinates of a point after a 90-degree clockwise rotation?

Back

To find the coordinates of a point (x, y) after a 90-degree clockwise rotation, the new coordinates will be (y, -x).

Front

What is the scale factor in dilation?

Back

The scale factor in dilation is a number that describes how much a figure is enlarged or reduced. It is found by dividing a prime coordinate by the original coordinate.

Front

What is the rule for translation?

Back

The rule for translation can be expressed as (x+a, y+b), where 'a' and 'b' are the horizontal and vertical shifts, respectively.

Front

What is the rule for reflection over the x-axis?

Back

The rule for reflection over the x-axis is to change the sign of the y-coordinate. For a point (x, y), the new coordinates will be (x, -y).