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Reflection in Geometry

In geometry, we often study about reflection. A figure is said to be the reflection of another if every point in one is at equal distance from each corresponding point in another. In this way, one is said to be the mirror image of another. In the language of set theory, reflection is said to be the mapping of a function onto itself. Reflection is type of transformation. It forms the mirror image of the object. The point of reflection is formulated simply through a recognized point or line. In a reflection of a point, the fundamental ideas of reflection are the transformation of a position to a reflected point to be the corresponding length of the conflicting sides of a line.

In reflection translation also takes place because it changes its position also. The reflection may be in reference with X and Y axis. If the mirror line or central line is the X axis, then the reflection of a point whose coordinates are (x , y) would be (x , -y). Similarly, when the mirror or central line is the Y axis, the reflection of the point with coordinates (x , y) will be (-x , y). In this article, we are going to learn about reflection in geometry. Now we shall study about reflection translation.

 

What is Reflection in Geometry

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Reflection is also called Flip. A reflection is nothing but the mirror image of the figure or shape. It will reflect the figure through a line, which is known as line of reflection. Reflection is nothing but we draw two figure on a plane paper and we fold the paper one figure overlap on the another figure so here each figure is a reflection of each other, and from where the paper was folded this is called line of reflection.It will be more clear with an examples. That are following.

Examples:

Horizontal and Vertical Reflection

Reflection structures as follows the given procedures:

Step 1:

Find the distance from the recognized object of a position to the necessary line L or mirror line.

Step 2:

Plot the reflected position on the opposed side of line L. Reflected location P' from an corresponding distances of a line L or mirror line.

Step 3:

Obtain the reflected form of point with formation the reflected shape.

Example:

Reflected form of point

Reflection Geometry Examples

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Below are the examples on math reflection :

Problem 1:

A triangle is given ABC, As shown is the figure. it will reflect along Y-axis. so draw the reflected figure ?

Math reflection

Solution:

Triangle are given ABC. and it reflect along Y-axis.

so, Y-axis is Line of reflection

Step 1:

At first we measure nearest distance between Line of reflection and a point of figure. Here A and C are the nearest points.

Step 2:

So we keep points on the same distance from line of reflection but is opposite side. Here we give the name of reflected ponts are A' and C'.

Step 3:

Reflect the third point along the line of reflection so here point B known as B'

Step 4:

We repeat the step 2 again and again untill to the last point of the figure. So the reflected figure is below

Reflection graph

Problem 2: A rectangular is given ABCD, As shown is the figure. it will reflect along X-axis. so draw the reflected figure.
Reflection geometry example

Solution:

Rectangular are given ABCD. and it reflect along X-axis.

so, X-axis is Line of reflection

Step 1:

At first we measure nearest distance between Line of reflection and a point of figure. Here C and D are the nearest points.

Step 2:

So we keep points on the same distance from line of reflection but is opposite side. Here we give the name of reflected ponts are C'and D'.

Step 3: Reflect the third point along the line of reflection, so here point B known as B'

Step 4: We repeat the step2 again and again untill to the last point of the figure. so the reflected figure is below

Reflection graph example

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