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Mathematics

Grade 9

Quadrilaterals, perspective drawing,transformations

Module 25

Understand and use the principle of translation, learning suitable notations

Having fun with plane shapes

ACTIVITY 1

To understand and use the principle of translation, learning suitable notations

[LO 3.2, 3.7]

Transformation through translation

Above we have the first quadrant of a Cartesian plane . There are ten plane figures to be seen.

If you imagine that you cut out the shaded shapes above, and then move them to new positions (unshaded) by sliding them across the page, then you have translated them. Notice that they stay upright (they don’t change their orientation ). These shapes have been transformed through translation.

  • Write down the names of the five shapes.

If you label the vertices of the shape, then the new position has similar (but not the same) labels. You can see this on the rectangle above. From now on, you will use the same system of labels in your work. In the rectangle, position A moves to position A, B to B, etc.

We have different ways of describing translations. This is like giving someone instructions so that they can produce the result you want.

1. For instance, if I say, “Move the oval shape 4½ units right and 3 units down,” this gives the new position of the oval.

  • Describe the new position of the pentagon in the same way in words.

2. Translating the square:

Square ABCD → square ABCD means map square ABCD onto square ABCD. This is better said by specifying the positions: A (1 ; 9) → A (5 ; 8) and B(4 ; 9) → B(8 ; 8), etc.

  • Use the coordinate mapping system to describe the translation of the triangle. Label the vertices A, B and C.

3. We can also say how far the shape must move in a certain direction, which we can specify as a compass bearing . This says how many degrees (navigators normally use three figures) clockwise we turn from due north. Refer to the figure. You can see that east is at 090° and west is at 270°. The line is at approximately 200°. The triangle above is 5 units away on a bearing of 090°. In other words, if you are at the top vertex of the triangle, you can see the new position of the top vertex 5 units away if you look east.

  • Use distance and bearing to translate the parallelogram above.
  • Give the shapes below (A to E) their proper names, label their vertices, and then draw them on this grid, translated to their new positions according to the descriptions below. Finally label the “new” vertices properly. Hint: work in pencil until you are sure!

A 21 units right and 3 units down

B 11 units on a bearing of 090°

C 20 units left and 6 units down

D (31 ; 4) → (11 ; 6), (34 ; 4) → (14 ; 6), (31 ; 1) → (11 ; 3) and (34 ; 1) → (14 ; 3)

E 7 units on a bearing of 270° followed by 4 units on a bearing of 180°

ACTIVITY 2

To understand and apply reflection

[LO 3.2, 3.7]

Transformation through reflection

Look again at the last problem (E) in the previous section. Can you see that it actually gives us two translations, one after the other? The descriptions for A and C do the same! This will happen again, as it is often the simplest way to describe a complicated transformation of a shape.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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