Hello Punch

From the diagram, we can see that represents a movement which can be described as:Move 1 unit to the right and 3 units down.

We can write this asSimilarly represents the movement:Move 2 units to the right and 2 units up

or:We add two movement (or displacement) vectors together using an ordinary sign, by thinking of as representing the phrase 'and then'. So meansMove 1 unit to the right and 3 units downand then

Move 2 units to the right and 2 units up

which is obviously equivalent toMove 3 units to the right and 1 unit down

We sometimes write all of this as:Do you see how it works?

Now stands for:Move from to So if and we must start at the point , and carry out the movement . When we do this, we get to the point . So that's where is: .

Now is the same movement as , but multiplied by . In other words:So: (Check this carefully!)

and this is the movement . So, to find the position of the point , start at and carry out the movement . Can you see that is at ?

Grandad