Quick Notes

Quick Notes

Mathematics Chapter 11: Isometric Transformations
11.2 Translation
 
11.2  Translation
 
  Definition  
     
 

The transfer of all points on a plane in the same direction and through the same distance.

  
   
         
Representation of translation in the form of vector:    
         
  • Vector of translation is a movement that has direction and magnitude and is determined based on the value and direction of a vector. 
    
         
Translation can be described using two methods,    
         

(i)

  

The direction of movement: to the right, left, upwards or downwards

    
       
 

The direction of distance: number of units

    
         

(ii)

  

Written in a vector form \(\dbinom{a}{b}\)

    
         
Image and object under a translation:    
         
Example    
         

   
     
  • \(M'\) is the image of object \(M\).
  • The translation is \(\dbinom{-4}{3}\).
    
         

Determining the coordinate of the image when coordinate of the object is given:
         
  • To locate the image with translation \(\dbinom{a}{b}\), the coordinate of object \((x,y)\) will be mapped to image \((x+a, y+b)=(x',y')\).
    
         

Two alternative methods are:

    
  • \(\dbinom{a}{b} + \dbinom{x}{y} = \dbinom{a+x}{b +y}\)
    
     
  • \(\dbinom{a}{b} - \dbinom{x}{y} = \dbinom{a-x}{b -y}\)
    
         

Determining the coordinate of the object when the coordinate of the image is given:
         
  • To locate an object with translation \(\dbinom{a}{b}\), the coordinate of image \((x',y')\) will be mapped to object \((x'-a, y'-b)=(x,y)\).
    
         

The alternative method is:

    
     
  • \(\dbinom{x}{y} = \dbinom{x'}{y'} - \dbinom{a}{b} \)
    
         

Defining vector translation when the position of image and object is given:

    
         

Given object \((x,y)\) and the image \((x',y')\).

\(\text{Vector Translation} = \dbinom{x' -x}{y' -y}\)