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Transformations - enrichment, not in caps

In this section you will learn about how the co-ordinates of a point change when the point is moved horizontally and vertically on the Cartesian plane. You will also learn about what happens to the co-ordinates of a point when it is reflected on the x -axis, y -axis and the line y = x .

Translation of a point

When something is moved in a straight line, we say that it is translated . You will recall that the term 'translation' was also mentioned in the section on functions to refer to what happens when an entire function is shifted in a straight line. What happens to the co-ordinates of a point that is translated horizontally or vertically?

Discussion : translation of a point vertically

Complete the table, by filling in the co-ordinates of the points shown in the figure.

Point x co-ordinate y co-ordinate
A
B
C
D
E
F
G

What do you notice about the x co-ordinates? What do you notice about the y co-ordinates? What would happen to the co-ordinates of point A, if it was moved to the position of point G?

When a point is moved vertically up or down on the Cartesian plane, the x co-ordinate of the point remains the same, but the y co-ordinate changes by the amount that the point was moved up or down.

For example, in [link] Point A is moved 4 units upwards to the position marked by G. The new x co-ordinate of point A is the same ( x =1), but the new y co-ordinate is shifted in the positive y direction 4 units and becomes y =-2 +4 =2. The new co-ordinates of point A are therefore G(1;2). Similarly, for point B that is moved downwards by 5 units, the x co-ordinate is the same ( x = - 2 , 5 ), but the y co-ordinate is shifted in the negative y -direction by 5 units. The new y co-ordinate is therefore y =2,5 -5 =-2,5.

Point A is moved 4 units upwards to the position marked by G. Point B is moved 5 units downwards to the position marked by H.
If a point is shifted upwards, the new y co-ordinate is given by adding the shift to the old y co-ordinate. If a point is shifted downwards, the new y co-ordinate is given by subtracting the shift from the old y co-ordinate.

Discussion : translation of a point horizontally

Complete the table, by filling in the co-ordinates of the points shown in the figure.

Point x co-ordinate y co-ordinate
A
B
C
D
E
F
G

What do you notice about the x co-ordinates? What do you notice about the y co-ordinates?

What would happen to the co-ordinates of point A, if it was moved to the position of point G?

When a point is moved horizontally left or right on the Cartesian plane, the y co-ordinate of the point remains the same, but the x co-ordinate changes by the amount that the point was moved left or right.

For example, in [link] Point A is moved 4 units right to the position marked by G. The new y co-ordinate of point A is the same ( y =1), but the new x co-ordinate is shifted in the positive x direction 4 units and becomes x =-2 +4 =2. The new co-ordinate of point A at G is therefore (2;1). Similarly, for point B that is moved left by 5 units, the y co-ordinate is the same ( y = - 2 , 5 ), but the x co-ordinate is shifted in the negative x -direction by 5 units. The new x co-ordinate is therefore x =2,5 -5 =-2,5. The new co-ordinates of point B at H is therefore (-2,5;1).

Questions & Answers

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s.
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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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.
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Graphene has a hexagonal structure
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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