Question

Can you help me apply the dilation to the polygon with the given vertices. Name the coordinates of the points. Identify and describe the transformation

Answer 1

Name the coordinates of the points. Identify and describe the transformation:

(4)

`D\colon(x,y)\longrightarrow(3x,3y)`

multiply each x value by 3 and also multiply each y value by 3

`\begin{gathered} A(0,0) \\ B(1,2) \\ C(3,-2) \end{gathered}`

`\begin{gathered} A(0,0)\longrightarrow A^1(0*3,0*3)=A^1(0,0) \\ B(1,2)\longrightarrow B^1(1*3,2*3)=B^1(3,6) \\ C(3,-2)\longrightarrow C^1(3*3,-2*3)=C^1(9,-6) \end{gathered}`

Hence the transformation reduces by three of the original coordinates

(5)

`D\colon(x,y)\longrightarrow(0.5x,0.5y)`

multiply each x value by 0.5 and also multiply each y value by 0.5

`\begin{gathered} A(10,6) \\ B(8,-4) \\ C(-2,0) \end{gathered}`

`\begin{gathered} A(10,6)\longrightarrow A^1(10*0.5,6*0.5)=A^1(5,3) \\ B(8,-4)\longrightarrow B^1(8*0.5,-4*0.5)=B^1(4,-2) \\ C(3,-2)\longrightarrow C^1(3*0.5,-2*0.5)=C^1(1.5,-1) \end{gathered}`

Hence the transformation reduces by half of the original coordinates