Question Number 104744 by mathocean1 last updated on 23/Jul/20
![ABCD is a square with center O. I is the middle of [BC]. 1) q is geometric transformation defined by q: M→M′ such that CM′^(→) =CM^(→) +3DM^(→) . a)Determinate the invariant point of q. b) show that q is a homothety and precise it ratio.](Q104744.png)
$${ABCD}\:{is}\:{a}\:{square}\:{with}\:{center}\:{O}. \\ $$$${I}\:{is}\:{the}\:{middle}\:{of}\:\left[{BC}\right]. \\ $$$$\left.\mathrm{1}\right)\:{q}\:{is}\:{geometric}\:{transformation} \\ $$$${defined}\:{by}\:{q}:\:{M}\rightarrow{M}'\:{such}\:{that} \\ $$$$\overset{\rightarrow} {{CM}'}=\overset{\rightarrow} {{CM}}+\mathrm{3}\overset{\rightarrow} {{DM}}. \\ $$$$\left.{a}\right){Determinate}\:{the}\:{invariant}\:{point} \\ $$$${of}\:{q}. \\ $$$$\left.{b}\right)\:{show}\:{that}\:{q}\:{is}\:{a}\:{homothety}\:{and}\: \\ $$$${precise}\:{it}\:{ratio}. \\ $$