System of reference in a plane

and

Application of vectors to geometric problems I
Block:Geometry
 
1. System of reference in a plane
In the set R = {O, (x,y)}  O fixed point, called the origin
 (x,y) base

AT EACH POINT P IN THE PLANE associated with ITS POSITION VECTOR OP WHICH HAS COORDINATES

The point P gives rise to the vector OP 

The vector OP has the coordinates (4,3) with respect to the base B(x,y) 

The point P has the coordinates (4,3) with respect to the system of reference R .

 

1.-Change the values of a and b and you can see how at another point P corresponds to another vector OP. 

2.- Observe how the coordinates of OP(a,b), will always be the coordinates of P(a,b).
2.   Application of vectors to geometric problems:   
2.1 COORDINATES OF THE VECTOR WHICH JOINS TWO POINTS  
In this figure there are three vectors which satisfy: OA + AB = OB. Therefore: AB = OB - OA  and it follows that

the coordinates of OA = coordinates of A  and the coordinates of OB = coordinates of B resulting in:

 coordinates of the vector AB = coordinates of the furthest point B - coordinates of its origin A 
1.- Try moving the points A and B (in this figure we have limited the movement of these points such that the vector AB always has the same direction) the coordinates of the vector AB.

2.- At the start of the previous figure we saw that AB = (3,-6) What are the coordinates of its furthest point B and of its origin A?.If we interchange the furthest point for its origin we will obtain a new vector "AB"( vector BA) What will be its coordinates? Make a note in your exercise book.
Help: Place the point A where B is and vice versa
3.- Now change the coordinates of the points A and B to those given in the box below. Make a note of them, calculate the coordinates of the vector AB in each case and then try them in the figure: 
A=(4,8) 
B=(6,4)		   AB=?  A=(8,0) 
B=(5,6)		   AB=? 
A=(5,6) 
B=(7,2)		   AB=?  A=(6,4) 
B=(6,4)		   AB=? 
       
           
  Ángela Núñez Castaín
 
Ministry of Education, Social Afairs and Sport. Year 2001
 
 

Licencia de Creative Commons
Except where otherwise noted, this work is licensed under a Creative Common License