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Definition |
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The transfer of all points on a plane in the same direction and through the same distance.
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| Representation of translation in the form of vector: |
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- Vector of translation is a movement that has direction and magnitude and is determined based on the value and direction of a vector.
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| Translation can be described using two methods, |
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(i)
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The direction of movement: to the right, left, upwards or downwards
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The direction of distance: number of units
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(ii)
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Written in a vector form \(\dbinom{a}{b}\)
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| Image and object under a translation: |
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| Example |
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- \(M'\) is the image of object \(M\).
- The translation is \(\dbinom{-4}{3}\).
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Determining the coordinate of the image when coordinate of the object is given:
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- To locate the image with translation \(\dbinom{a}{b}\), the coordinate of object \((x,y)\) will be mapped to image \((x+a, y+b)=(x',y')\).
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Two alternative methods are:
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- \(\dbinom{a}{b} + \dbinom{x}{y} = \dbinom{a+x}{b +y}\)
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- \(\dbinom{a}{b} - \dbinom{x}{y} = \dbinom{a-x}{b -y}\)
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Determining the coordinate of the object when the coordinate of the image is given:
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- To locate an object with translation \(\dbinom{a}{b}\), the coordinate of image \((x',y')\) will be mapped to object \((x'-a, y'-b)=(x,y)\).
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The alternative method is:
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- \(\dbinom{x}{y} = \dbinom{x'}{y'} - \dbinom{a}{b} \)
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Defining vector translation when the position of image and object is given:
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Given object \((x,y)\) and the image \((x',y')\).
\(\text{Vector Translation} = \dbinom{x' -x}{y' -y}\)
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