# REFLECTION TRANSFORMATION IN GEOMETRY

## About the topic "Reflection transformation in geometry"

"Reflection transformation" is one of the four types of transformations in geometry.

Even though students can get this stuff on internet, they do not understand exactly what has been explained.

To make the students to understand the stuff "Reflection-transformation", we have explained the different rules which we apply to make reflection-transformation.

## Reflection about the line y=x

Once students understand the rules which they have to apply for reflection transformation, they can easily make reflection -transformation of a figure.

For example, if we are going to make reflection transformation of the point (2,3) about x-axis, after transformation, the point would be (2,-3). Here the rule we have applied is (x, y) ------> (x, -y).

So we get (2,3) -------> (2,-3).

Let us consider the following example to have better understanding of reflection.

Question :

Let A ( -2, 1), B (2, 4) and (4, 2) be the three vertices of a triangle. If this triangle is reflected about x-axis, what will be the new vertices A' , B' and C' ?

Solution:

Step 1 :

First we have to know the correct rule that we have to apply in this problem.

Step 2 :

Here triangle is reflected about x - axis. So the rule that we have to apply here is (x , y) -------> (x , -y)

Step 3 :

Based on the rule given in step 1, we have to find the vertices of the reflected triangle A'B'C'

Step 4 :

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

A ( -2, 1 ) ------------ A' ( -2, -1 )

B ( 2, 4 ) ------------ B' ( 2, -4 )

C ( 4, 2 ) ------------ C' ( 4, -2 )

Step 5 :

Vertices of the reflected triangle are

A' ( -2, -1) , B ( 2, -4 ) and C' ( 4, -2)

## Reflecting over any line

When we look at the above figure, it is very clear that each point of a reflected image A'B'C' is at the same distance from the line of reflection as the corresponding point of the original figure.

In other words, the line x = -2 (line of reflection) lies directly in the middle between the original figure and its image.

And also, the line x = -2 (line of reflection) is the perpendicular bisector of the segment joining any point to its image.

Students can keep this idea in mind when they are working with lines of reflections which are neither the x-axis nor the y-axis.

After having gone through the stuff given above, we hope that the students would have understood "Reflection transformation".

If you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6