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**Related Pages**Properties of ReflectionTransformationMore lessons On Geometry

### What is Reflection?

In a **reflection** transformation, every the point out of an item are reflect or flippedon a line referred to as the **axis of reflection** or heat of reflection.

**Example:**

A enjoy is characterized by the **axis of symmetry** or **mirror line**. In the over diagram,the winter line is x = 3.

Under reflection, the shape and size of photo is exactly the same as the initial figure.This kind of change is referred to as **isometric** transformation.

The orientation is **laterally inverted**, the is castle are facing opposite directions.

The heat of enjoy is the perpendicular bisector the the heat joining any suggest and itsimage (e.g. PP ’ in the above figure).

All the point out on the mirror line space not changed. These points are said to be **invariant**.(R is an invariant suggest in the above.)

### Drawing The image on network Lines

If the axis of enjoy is on among the network lines, we simply count the variety of squaresfrom a allude on the thing to the axis and the picture is the same distance native the axis.

**Example:**In the diagram, the number A is reflected in the line XY. Attract the photo of A in the diagram.

**Solution:**

Note the the suggest O stayed unchanged under reflection due to the fact that it is ~ above the axis of reflection.Any allude on the heat of have fun is unchanged – such points are defined as invariant.

**How to reflect a form on squared document without utilizing tracing paper**This video shows how to reflect a shape on squared file without utilizing tracing paper. Justcount the street of each corner to the mirror line and count the very same distance far fromthe mirror line. Once all the points have actually been reflected them, join the points up neatlyusing her ruler.

### Draw the picture using a compass

If the axis of reflection is not on the grid lines, we will must use a compass to construct the image.

**Example:**

In the diagram below, the triangle alphabet is reflected in the heat XY. Attract the photo of thetriangle in the diagram.

**Solution:**Step 1: place the sharp allude of a compass in ~ A and draw twoarcs intersecting the heat XY

Step 2: location the sharp suggest of the compass on first intersecting allude and mark an arc ~ above the opposite next of XY. Location the spicy pointof the compass on the second intersecting point and note an arc come intersect v the firstarc. The intersection is the image of A’.

Step 3: Repeat measures 1 and 2 to acquire the clues B ’ and also C ’.Join the point out A ’ , B ’ and also C ’ to acquire the photo A ’ B ’ C ’.

**Construct reflection by Hand**How to reflect a figure over a line by hand utilizing a ruler.

**How to construct a heat of Reflection?**Construct a line of reflection given the object and also the image.

### Reflection ~ above the name: coordinates Plane

We will currently look at exactly how points and shapes room reflected on the name: coordinates plane. It will certainly behelpful to note the fads of the collaborates when the points are reflected over differentlines that reflection.

Coordinate Rules for ReflectionIf (a, b) is reflected on the x-axis, its image is the allude (a, -b)If (a, b) is reflect on the y-axis, its photo is the suggest (-a, b)If (a, b) is reflect on the heat y = x, its image is the point (b, a)If (a, b) is reflected on the heat y = -x, its image is the point (-b, a)

Geometry enjoy A have fun is an isometry, which method the original and also image space congruent, that can bedescribed as a “flip”. To do a geometry reflection, a line of enjoy is needed;the result orientation of the two figures are opposite. Matching parts that thefigures room the same distance from the heat of reflection. Ordered pair rules reflect overthe x-axis: (x, -y), y-axis: (-x, y), line y = x: (y, x).

This video shows reflection over the x-axis, y-axis, x = 2, y = −2

This video clip shows reflection over y = x, y = − x. A enjoy that results in an overlapping shape.

This video shows reflection over the x-axis, y-axis, x = −3, y = 5, y = x, and y = − x.

### Reflections using Matrices

This lesson involves reflections in the coordinate plane. We use coordinate rules as wellas matrix multiplication come reflect a polygon (or polygon matrix) about the x-axis,y-axis, the heat y = x or the heat y = -x.

Matrices and ReflectionsPerforming reflections with matrices end the y-axis and also x-axis.

Matrices for Reflections over the y-axis and x-axis.

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Matrices for Reflections over the heat y = x.

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