Question

finding a vertex of the pre - image
given the dilation rule ( d_{o,1/3}(x,y)\to(\frac{1}{3}x,\frac{1}{3}y) )
and the image ( stuv ), what are the coordinates of
vertex ( v ) of the pre - image?
( (0,0) )
( (0,\frac{1}{3}) )
( (0,1) )
( (0,3) )

Explanation:

Step1: Determine the coordinates of \(V'\)

From the graph, the coordinates of \(V'\) are \((0,1)\).

Step2: Use the dilation rule to find the pre - image

The dilation rule is \(D_{O,\frac{1}{3}}(x,y)\to(\frac{1}{3}x,\frac{1}{3}y)\). Let the coordinates of \(V\) be \((x,y)\). Then \(\frac{1}{3}x = 0\) and \(\frac{1}{3}y=1\).
For \(x\):

$$
LATEXBLOCK0
$$

For \(y\):

$$
LATEXBLOCK1
$$

Answer:

\((0,3)\)