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}`