Question

Identify the scale factor that was used to graph W' X' Y'

Answer 1

Given triangle WXY with coordinates

`W(3,4),X(12,10),Y(6,-2)`

The image W'X'Y' has coordinates

`W^(\prime)(2,1),X^(\prime)(8,5),Y^(\prime)(4,-3)`

According to the image coordinates,the dilation is negative, the image has been translated downward also, therefore the scale factor and the translation unit is

`\begin{gathered} \text{Dilation rule} \\ (x,y)\Rightarrow(1)/(k)(x^(\prime),y^(\prime)) \end{gathered}`
`\begin{gathered} W(3,2)\Rightarrow W^(\prime)((2)/(k),(1)/(k)) \\ \text{Hence } \\ (2)/(k)=3 \\ 3k=2 \\ k=(2)/(3) \end{gathered}`
`\begin{gathered} \text{the dowward shift } \\ W^(\prime)(x^(\prime),y^(\prime)+h)\Rightarrow(8,5+h)\Rightarrow((2)/(3)(12,10) \\ \text{Thus} \\ 5+h=(20)/(3) \\ h=(20)/(3)-5=(20-15)/(3)=(5)/(3) \end{gathered}`

Therefore the general rule is

`(2)/(3)(x,y-(5)/(3))\Rightarrow(x^(\prime),y^(\prime)_{})`

Hence, the scale factor is 2/3