<< Chapter < Page Chapter >> Page >

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).

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 10 maths [caps]' conversation and receive update notifications?

Ask