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 Geometry Transformations Geometry Translation A translation is an isometry that moves a shape by sliding it up, down, sideways or diagonally. without turning it or making it bigger or smaller. ABC has been translated to A'B'C' by moving 4 squares to the right and the 2 squares up. This translation is written as a vector $\fs2A=\left(\begin{matrix}4\\2\end{matrix}\right)$ Sometimes we just want to write down the translation, without showing it on a graph. If we want to say that the shape gets moved 3 units in the "x" direction and 4 units in the "y" direction, we can write: (x,y) $\rightarrow$ (x+3,y+4) This says "all the x and y coordinates will become x+3 and y+4" Find the new image of triangle ABC using the translation: $(x,y)\rightarrow\;(x-2,y+3)$ Solution: A(1,1) $\rightarrow\;$ A'(1,-4) B(6,5) $\rightarrow\;$ B'(4,8) C(7,1) $\rightarrow\;$ C'(5,4) Write a rule to describe the translation: Let's see that Y(4,1) $\rightarrow\;$ Y'(-6,-2) Then, the rule is: (x,y) $\rightarrow$ (x - 10, y - 3)