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# Graph the image of the figure after a dilation with a scale factor of 2 centered at (−2, −2) .

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Graph the image of the figure after a dilation with a scale factor of 2 centered at (−2, −2) .

Jan 26, 2018

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Graph the image of the figure after a dilation with a scale factor of 2 centered at (−2, −2) .

$$\begin{array}{lrcll} \text{Formula dilation:} & \boxed{\vec{A}' = (\vec{A}-\vec{C_{Center}})\cdot \lambda +\vec{C_{Center}}} \\ & \vec{A} \text{ before dilation } & \text{\lambda scale factor } = 2 \\ & \vec{A}' \text{ after dilation } & \text{\vec{C_{Center}} center at \binom{-2}{-2}  } \\ \end{array}$$

$$\begin{array}{lrcll} &\vec{A}' &=& (\vec{A}-\vec{C_{Center}})\cdot \lambda +\vec{C_{Center}}\\ & &=& \vec{A}\cdot \lambda +\vec{C_{Center}}\cdot (1-\lambda ) \\ & &=& \lambda \cdot \vec{A} +(1-\lambda )\cdot \vec{C_{Center}} \\ \text{Formula dilation:} & \boxed{\vec{A}' =\lambda \cdot \vec{A} +(1-\lambda )\cdot \vec{C_{Center}}} \\ & (1-\lambda )\cdot \vec{C_{Center}} &=& (1-2)\binom{-2}{-2} \\ & (1-\lambda )\cdot \vec{C_{Center}} &=& (-1)\binom{-2}{-2} \\ & (1-\lambda )\cdot \vec{C_{Center}} &=& \binom{2}{2} \\ \end{array}$$

$$\begin{array}{lrcll} \boxed{\vec{A}'=\lambda \cdot \vec{A} +\binom{2}{2}}& \vec{A} = \dbinom{-4}{-2}\\ \boxed{\vec{B}'=\lambda \cdot \vec{B} +\binom{2}{2}}& \vec{B} = \dbinom{-5}{2}\\ \boxed{\vec{C}'=\lambda \cdot \vec{C} +\binom{2}{2}}& \vec{C} = \dbinom{-1}{3}\\ \boxed{\vec{D}'=\lambda \cdot \vec{D} +\binom{2}{2}}& \vec{D}= \dbinom{1}{1}\\ \end{array}$$

$$\begin{array}{lrcll} \boxed{\vec{A}'=2 \cdot \binom{-4}{-2} +\binom{2}{2}}& \vec{A}' = \dbinom{-6}{-2}\\ \boxed{\vec{B}'=2 \cdot \binom{-5}{2} +\binom{2}{2}}& \vec{B}' = \dbinom{-8}{6}\\ \boxed{\vec{C}'=2 \cdot \binom{-1}{3} +\binom{2}{2}}& \vec{C}' = \dbinom{0}{8}\\ \boxed{\vec{D}'=2 \cdot \binom{1}{1} +\binom{2}{2}}& \vec{D}' = \dbinom{4}{4}\\ \end{array}$$

Point (-4, -2 ) goes to (-6,-2)

Point (-5, 2) goes to (-8. 6)

Point ( -1, 3) goes to (0, 8)

Point ( 1, 1 ) goes to (4, 4 )

Jan 26, 2018
edited by heureka  Jan 26, 2018