Question

Leon designs a fabric pattern using figure STUVW. He dilates figure STUVW using a scale factor of 2 with a center of dilation at vertex V to form figure STUVW. Then Leon rotates this image 90' clockwise around the origin to form figure STUVW". What are the coordinates of figure STUVW?

Answer 1

The formula for dilation about a point (h, k) is given by

$(x,y)\rightarrow(h+t(x-h),k+t(y-k))$

We are dilating the figure by a factor of 2 about vertex V(0,1 ); therefore, the coordinate transfromations will be

$S(0,5)\rightarrow S^{\prime}(0,9)_{}$$\begin{gathered} T(3,5)\rightarrow T^{\prime}(6,9) \\ U(3,1)\rightarrow U^{\prime}(6,1) \\ V(0,1)\rightarrow V^{\prime}(0,1) \\ W(2,3)\rightarrow W^{\prime}(4,5) \end{gathered}$

Finally, roatiing these coordinates 90 degree clockwise gives us

$(x,y)\rightarrow(y,-x)$$\begin{gathered} S^{\prime}(0,9)\rightarrow\textcolor{#FF7968}{S^{\doubleprime}(9,0)} \\ T^{\prime}(6,9)\rightarrow\textcolor{#FF7968}{T^{\doubleprime}(9,-6)} \\ U^{\prime}(6,1)\rightarrow\textcolor{#FF7968}{U^{\doubleprime}(1,-6)} \\ V^{\prime}(0,1)\rightarrow\textcolor{#FF7968}{V^{\doubleprime}(1,0)} \\ W^{\prime}(2,3)\rightarrow\textcolor{#FF7968}{W^{\doubleprime}(3,-2)} \\ \end{gathered}$