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UNIT
14
14.1: Translate a Figure
Graph the image given the preimage and the translation rule.

The image of \(\triangle ABC\) is \(\triangle A'B'C'\). Graph and label \(\triangle A'B'C'\) after the translation \(( x,\;y)\longrightarrow (x \;+\; 6 ,\; y\; +\; 4)\).
Find the translation rule that maps the preimage to the image.

Find the rule that translates quadrilateral \(ABCD\) to quadrilateral \(A'B'C'D'\).
Perform 2 consecutive translations.

\(\triangle ABC\) is translated to \(\triangle A'B'C'\) by the rule \((x ,\; y) \longrightarrow (x \;+\; 7 ,\; y\; -\; 2)\).
\(\triangle A'B'C'\) is translated to \( \triangle A'' B'' C'' \) by the rule \((x ,\; y) \longrightarrow (x\; -\; 4 ,\; y\; +\; 3)\).
Find the coordinates of \(A'' ,\; B''\) and \(C''\), given

\(A(-3 ,\; 6) ,\; B(-1 ,\; 2),\; C(8 ,\; 2)\)