Write a rule to describe the
translation of a point given P(-1, 5)
and P’(0,9).

In geometry we use input/output process when we determine how shapes are altered or moved. Geometric objects can be moved in the coordinate plane using a coordinate rule. These rules can alter the shape in many different ways. Some rules will translate the shape, some will rotate or reflect the shape, some will stretch or distort the shape, some will increase the size of the shape, etc... lots of different things can happen. Look at the example below:

So rule T will move or map all points (x,y) by adding 3 to the x value of each point, and subtracting 6 from each y value of each point

 The name of the rule is a capital letter before the (x,y). The point (x,y) represents that all points in the plane will be effected by this rule. The arrow represents the geometric term of map or mapping, which is a geometric way of saying moves. Finally the coordinate description after the mapping arrow symbol represents the change produced by the rule. Can you see the connection to functions? You will input values into the coordinate rule and it will output new values, just as function did. A change is that we refer to the input value as the pre-image, the original location of the point, and the output value as the image, the new location of the point.