# 9.3 Transformations  (Page 2/3)

 Page 2 / 3 Point A is moved 4 units to the right to the position marked by G. Point B is moved 5 units to the left to the position marked by H.
If a point is shifted to the right, the new $x$ co-ordinate is given by adding the shift to the old $x$ co-ordinate. If a point is shifted to the left, the new $x$ co-ordinate is given by subtracting the shift from the old $x$ co-ordinate.

## Reflection of a point

When you stand in front of a mirror your reflection is located the same distance ( $d$ ) behind the mirror as you are standing in front of the mirror.

We can apply the same idea to a point that is reflected on the $x$ -axis, the $y$ -axis and the line $y=x$ .

## Reflection on the $x$ -axis

If a point is reflected on the $x$ -axis, then the reflection must be the same distance below the $x$ -axis as the point is above the $x$ -axis and vice-versa, as though it were a mirror image. Points A and B are reflected on the x -axis. The original points are shown with • and the reflected points are shown with ∘ .
When a point is reflected about the $x$ -axis, only the $y$ co-ordinate of the point changes.

Find the co-ordinates of the reflection of the point P, if P is reflected on the $x$ -axis. The co-ordinates of P are (5;10).

1. We are given the point P with co-ordinates (5;10) and need to find the co-ordinates of the point if it is reflected on the $x$ -axis.

2. The point P is above the $x$ -axis, therefore its reflection will be the same distance below the $x$ -axis as the point P is above the $x$ -axis. Therefore, $y$ =-10.

For a reflection on the $x$ -axis, the $x$ co-ordinate remains unchanged. Therefore, $x$ =5.

3. The co-ordinates of the reflected point are (5;-10).

## Reflection on the $y$ -axis

If a point is reflected on the $y$ -axis, then the reflection must be the same distance to the left of the $y$ -axis as the point is to the right of the $y$ -axis and vice-versa. Points A and B are reflected on the y -axis. The original points are shown with • and the reflected points are shown with ∘ .
When a point is reflected on the $y$ -axis, only the $x$ co-ordinate of the point changes. The $y$ co-ordinate remains unchanged.

Find the co-ordinates of the reflection of the point Q, if Q is reflected on the $y$ -axis. The co-ordinates of Q are (15;5).

1. We are given the point Q with co-ordinates (15;5) and need to find the co-ordinates of the point if it is reflected on the $y$ -axis.

2. The point Q is to the right of the $y$ -axis, therefore its reflection will be the same distance to the left of the $y$ -axis as the point Q is to the right of the $y$ -axis. Therefore, $x$ =-15.

For a reflection on the $y$ -axis, the $y$ co-ordinate remains unchanged. Therefore, $y$ =5.

3. The co-ordinates of the reflected point are (-15;5).

## Reflection on the line $y=x$

The final type of reflection you will learn about is the reflection of a point on the line $y=x$ .

## Casestudy : reflection of a point on the line $y=x$

Study the information given and complete the following table:

 Point Reflection A (2;1) (1;2) B (- $1\frac{1}{2}$ ;-2) (-2;-1 $\frac{1}{2}$ ) C (-1;1) D (2;-3)

what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Preparation and Applications of Nanomaterial for Drug Delivery
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
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