12.5 Drawing a Locus

A locus is a set of points that follow a given rule. The plural of locus is loci. You need a ruler and compass to draw a locus accurately

There are five basic locus theorems (rules). 

 Each theorem will be explained in detail in the following sections under this topic.  Even though the theorems sound confusing, the concepts are easy to understand.

When attempting to solve a locus problem, there are certain steps that should be followed:

reference: http://www.regentsprep.org/Regents/math/geometry/GL1/What.htm

12.4 Enlarging Shapes

When you enlarge a shape, all the lengths of the sides of the shape increase in the same proportion. This is called the scale factor. All the angles in the shape stay the same size.

When you describe an enlargement you must give:

• The scale factor of the enlargement.
• The position of the center of the enlargement

The picture above shows you how an enlarged shape looks like. This one is a triangle. Unlike tessellating shapes, you can enlarge any shapes to any size. 

The opposite of enlargement is reduction.

12.3 Transforming Shapes

You can use a combination of reflections, translations and rotations to transform a shape. You can also describe the transformation that maps an object onto its image.

To describe a reflection you must give: 

• the equation of the mirror line

To describe a translation you must give: 

• the column vector
  
  

To describe a rotation you must give: 

• the centre of rotation

•  the number of degrees of rotation (or fraction of whole turn)

• the direction of the reaction (clockwise or anticlockwise)

12.2 Solving trasnformations problem

 you may want to copy the grid on your book or do the questions on grid paper! :D

12.1 Tessellating Shapes

A tessellation is a pattern made of identical shapes. You can make your own tessellations by fitting copies of a shape together, without gaps or overlaps. 

You say that the shape tessellates, or is a tessellating shape. 

Here are some examples of shapes that tessellate with themselves. 

Here are some examples of shapes that do not tessellate with themselves. There are gaps between the shapes. 

When you make a tessellation you can move the shape by translating, rotating or reflecting it.
For example, here are some of the ways you can tessellate a rectangle. 

Many tesselations are made by repeating a shape and using half-turn rotations of the same shape.

For example, a normal triangle and a half-turn rotation of the same triangle fit together perfectly to make a tessellation like this:

In any tessellations, the sum of the angles at the point where the vertices of the shape meet is 360°.

Look closely the tessellation below:

90° + 90° + 90° + 90° = 360°

Worked Example 12.1

a. Show that the triangle below will tessellate by drawing a tessellation on squared paper.

b. Explain why a regular pentagon will not tessellate. 

Answer:

Water Cleaning Project

FAPIPS Water Cleaning Organization from Al-Taqwa College Indonesia would like to introduce our plan

Program: Water Cleaning

Name of organization: FAPIPS water cleaning

Slogan: Air bersih, kita senang.

Aim: We want to help the people who live
nearby the Citarum river get clean water.

Location: Citarum River, Bekasi, Indonesia

How to reach there: Voluntary transportation with the help of google map

Reason: The people of Citarum are lacking
of clean water.

Problem: Citarum river is covered in
rubbish so that no clean water can be obtain.

Solution: Clean the river from the rubbish.

Steps:

1. Persuade the society to cooperate by stop littering.
2. Pick up all the rubbish in the river in order to clean it.
3. Cooperate with a company in Citeureup to recycle the rubbish.
4. Get a sponsor.
5. Cooperate with the government to support our program.

((FAPIPS stands for Fatimah, Angela, Putri, Indah, Prstina, Shoffa. These are the members.)

What Should You Do as the Next President?

Dear Mr. Prabowo,

Our names are Indah and Pristina. We would like to ask you some questions since we know that you are one of the nominees of Indonesia’s Next Presidents.

As we know that Indonesia is going to have a democracy party on April 9 2014. Every citizen has the right to choose their own choice for a leader. There are many president candidates that are willing to be presidents and you are one of them.

If you really are willing to be the next President of Indonesia, then we have some questions for you. 

Us, as Indonesian citizens surely want a leader who can develop Indonesia and make Indonesia as a better country.

1.  In your opinion, are you really sure to be the next president of Indonesia 2014-2019 that is going to be chose by the citizens through the election?

According to political observer from University of Indonesia, Andrinof Chaniago predicted that the amount of citizens who don’t take the right to vote their leader will increase.

“The amount of citizens who don’t take the right to vote can increase from 35 up to 40 percent.” said Andrinof when he was contacted by Kompas.

We think that this might be the proof that Indonesian citizens don’t care about the future of Indonesia. Do you think you can be the next president of Indonesia in this condition?

And then our next question is:

2.  What is the first thing that you will do when you become the president of Indonesia?

We know that being the president of Indonesia with 240 million citizens and many islands can’t be easy. To us, it’s very hard to just be a leader in the classroom. If being a leader in a classroom is hard, how about ruling millions of citizens from many tribes and cultures? We can’t imagine it, it must be really hard. It’s a big challenge.

We want the next president of Indonesia to not take the wrong step in every of his action and duty. The next president of Indonesia should be sure and aware of all the risks from his deed. We really want to have Indonesia developed. Just like Japan and Singapore. If Japan and Singapore can be developed then Indonesia should be able to be developed too!

The third question: 

3.Can you assure that when you become the next President of Indonesia, Indonesia will be free from corruption?

It's pathetic to see and hear the legendary and phenomenal news on the television until very recently. Whenever there is a new hot topic, it must be about corruption. Corruption news has been the trending topic of Indonesia. Indonesia must be lead by a leader who has a strong faith and iman. Corruption is a shameful act. Verily, corruption disadvantage not only oneself, but every citizen of Indonesia. If the next leader is a corruptor, what will happen to the future of Indonesia? One can't be a president of the country, if he can't even be a president to himself. A leader must be firm and be a role model to the citizens. 

It's an honor for us as students, if you can answer our 3 questions.

Because we hope that Indonesia will have a deserving President to lead Indonesia. So that one day, Indonesia can be a developed country.

Thank You. 

Sincerely,

Pristina and Indah.