# CORDINATE RULES FOR REFLECTIONS

A reflection is a transformation representing a flip of a figure. Figures may be reflected as following.

(i) In a point

(ii) In a line

(iii)  In a plane

The reflected image will be congruent to the original.

What is line of reflection ?

A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.

What is preimage ?

Preimage In a transformation, the original figure is called the preimage.

What is image ?

Image In a transformation, the final figure is called the image.

Reflections can be performed easily in the coordinate plane using the general rules below.

## Types of reflections

Reflection over x axis

Reflection over y axis

Reflection over y = x

Reflection over y = -x

## Rules

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

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

(x, y) ==> (y, x)

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

(x, y) ==> (-x, -y).

The rule of reflection about x-axis is

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

The rule of reflection about y-axis is

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

## Reflection about y = x

The rule of reflection about y = x is

(x, y) ==> (y, x)

## Reflection about y = -x

The rule of reflection about y = -x is

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

The rule of reflection about origin is

(x, y) ==> (-x, -y).

## Reflection about y = -2

To reflect the image about y = k, we have to draw the horizontal line through k.

Calculate the distance between every vertices on the given shape.

To get the reflected image, we have to go in the opposite direction with the distance.

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