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Geometry Transformations
Geometry Translation: Find the coordinates

When a point (x,y) undergoes a translation $\fs2A=\left(\begin{matrix}a\\b\end{matrix}\right)$, the image of (x,y) is (x + a, y + b)

Determine the image of P(5,-2) under the translation $\fs2A=\left(\begin{matrix}-4\\3\end{matrix}\right)$

 The image of P(5,-2) =[5+(-4),-2+3] =(1,1)

If (p,q) is the image of an object under a translation $\fs2A=\left(\begin{matrix}a\\b\end{matrix}\right)$, then the object is (p-a,q-b).

If (4,-3) is the image of P under the translation $\fs2A=\left(\begin{matrix}a\\b\end{matrix}\right)$. Find the coordinates of P.

 The coordinates of P =[4 - 5, -3-(-6)] =(-1,3)

Determine the image of P(-10,-5) of an object under a translation$\fs2A=\left(\begin{matrix}4\\2\end{matrix}\right)$

Solution: P*=(, )