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 coordinates of a point that is translated horizontally or vertically?
Complete the table, by filling in the coordinates of the points shown in the figure.
Table 3
Point

xx coordinate

yy coordinate

A 


B 


C 


D 


E 


F 


G 


What do you notice about the xx coordinates? What do you notice about the yy coordinates?
What would happen to the coordinates 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 xx coordinate of the point remains the same, but the yy coordinate changes by the amount that the point was moved up or down.
For example, in Item 19 Point A is moved 4 units upwards to the position marked by G. The new xx coordinate of point A is the same (xx=1), but the new yy coordinate is shifted in the positive yy direction 4 units and becomes yy=2+4=2. The new coordinates of point A are therefore G(1;2). Similarly, for point B that is moved downwards by 5 units, the xx coordinate is the same (x=2,5x=2,5), but the yy coordinate is shifted in the negative yydirection by 5 units. The new yy coordinate is therefore yy=2,5 5=2,5.
If a point is shifted upwards, the new yy coordinate is given by adding the shift to the old yy coordinate. If a point is shifted downwards, the new yy coordinate is given by subtracting the shift from the old yy coordinate.
Complete the table, by filling in the coordinates of the points shown in the figure.
Table 4
Point

xx coordinate

yy coordinate

A 


B 


C 


D 


E 


F 


G 


What do you notice about the xx coordinates? What do you notice about the yy coordinates?
What would happen to the coordinates 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 yy coordinate of the point remains the same, but the xx coordinate changes by the amount that the point was moved left or right.
For example, in Figure 44 Point A is moved 4 units right to the position marked by G. The new yy coordinate of point A is the same (yy=1), but the new xx coordinate is shifted in the positive xx direction 4 units and becomes xx=2+4=2. The new coordinate of point A at G is therefore (2;1). Similarly, for point B that is moved left by 5 units, the yy coordinate is the same (y=2,5y=2,5), but the xx coordinate is shifted in the negative xxdirection by 5 units. The new xx coordinate is therefore xx=2,5 5=2,5. The new coordinates of point B at H is therefore (2,5;1).
If a point is shifted to the right, the new xx coordinate is given by adding the shift to the old xx coordinate. If a point is shifted to the left, the new xx coordinate is given by subtracting the shift from the old xx coordinate.