How does the coordinate rule for making two similar shapes relate to the scale factor ?

To make two similar shapes, we use the coordinate rule. This means that for whatever we do to point x, we do the same to point y for every coordinate:

If our original point is (3,4) and we add 2 to 3, then we must also add 2 to 4: (3+2, 4+2) --> (5, 6). After doing this to all the coordinates, the shape on the graph will not have stayed the same, but it will have moved. 

The scale factor means that a number is used to multiply something else. Using the scale factor in relation to the coordinate rule, we can make a shape bigger by multiplying each coordinate by the same number:

If our original point is still (3,4), and we multiply 3 by 2, then we must also multiply 4 by 2: (3x2, 4x2) --> (6, 8). This way, the shape on the graph will have grown bigger. 

(6,0) i hope it makes enough sense