## 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 $$(x',y')$$.

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