Geometry Reflection, Translation & Rotation Formulas

Questions and Answers

What is the formula for reflection in the x-axis?

(x, y) -> (y, x)

(x, y) -> (x, -y) (correct)

(x, y) -> (-y, -x)

(x, y) -> (-x, y)

What is the formula for reflection in the y-axis?

(x, y) -> (-y, -x)

(x, y) -> (y, x)

(x, y) -> (-x, y) (correct)

(x, y) -> (x, -y)

What is the formula for reflection in y = x?

(x, y) -> (x, -y)

(x, y) -> (y, x) (correct)

(x, y) -> (-x, y)

(x, y) -> (-y, -x)

What is the formula for reflection in y = -x?

(x, y) -> (-y, -x) Signup and view all the answers

What is the formula for translation on a coordinate plane?

(x, y) -> (x+a, y+b) Signup and view all the answers

What is the formula for a 90 degree rotation?

(x, y) -> (-y, x) Signup and view all the answers

What is the formula for a 180 degree rotation?

(x, y) -> (-x, -y) Signup and view all the answers

What is the formula for a 270 degree rotation?

(x, y) -> (y, -x) Signup and view all the answers

Study Notes

Reflection Formulas

Reflection in the x-axis: Changes the y-coordinate's sign while keeping the x-coordinate the same, represented as (x, y) -> (x, -y).
Reflection in the y-axis: Changes the x-coordinate's sign while retaining the y-coordinate, detailed as (x, y) -> (-x, y).
Reflection in the line y = x: Swaps the x and y coordinates, noted as (x, y) -> (y, x).
Reflection in the line y = -x: Swaps and negates both coordinates, expressed as (x, y) -> (-y, -x).

Translation Formula

Translation on a coordinate plane: Moves a point horizontally and vertically by adding specific values to the coordinates, formulated as (x, y) -> (x + a, y + b).

Rotation Formulas

90-degree rotation: Converts coordinate (x, y) to (-y, x), effectively rotating the point counterclockwise.
180-degree rotation: Rotates points to the opposite direction in a straightforward manner, shown as (x, y) -> (-x, -y).
270-degree rotation: Turns points clockwise to (-y, x), altering their positions in the plane accordingly.

Description

Test your knowledge of important geometry transformations such as reflection, translation, and rotation with these flashcards. Each card provides a definition and formula for various types of transformations on a coordinate plane.