Question

AX'Y'Z' is a dilation of AXYZ Identify the type of dilation and find the scale factor. AY 7 6 5 N IY 4 2 Z' 1 X' 1 2 3 4 5 6 7 8 enlargement O reduction The scale factor is PREV 3 4 5 6 7 SUBMIT O 9

Answer 1

Dilation with center at origin is given by the formula

`\begin{gathered} D_(O,k)(x,y)=(kx,ky) \\ \text{Where O is the center of dilation at (0,0) and k is the scale factor} \end{gathered}`

So, in this case, you have

`\begin{gathered} X^(\prime)(0,0)\rightarrow X(0,0) \\ Y^(\prime)(0,4)\rightarrow Y(0,8) \\ Z^(\prime)(2,3)\rightarrow Z(4,6) \end{gathered}`

You can see that the value of k is 2 because

`\begin{gathered} X^(\prime)(0,0)\rightarrow X(2\cdot0,2\cdot0)=X(0,0) \\ Y^(\prime)(0,4)\rightarrow Y(2\cdot0,2\cdot4)=Y(0,8) \\ Z^(\prime)(2,3)\rightarrow Z(2\cdot2,2\cdot3)=Z(4,6) \end{gathered}`

Finally, since k > 1 then the dilation is an enlargement.