Answer:
The correct option is 4. The coordinates of preimage are [tex](\frac{7}{3},\frac{2}{3})[/tex].
Step-by-step explanation:
According to [tex]D_{O,3}[/tex], the figure dilated by scale factor 3 and he center of dilation is origin.
If a the scale factor is k and center of dilation is origin, then
[tex]P(x,y)\rightarrow P'(kx,ky)[/tex]
The scale factor is 3.
[tex]P(x,y)\rightarrow P'(3x,3y)[/tex]
Since the coordinates of image are (7,2).
[tex](3x,3y)=(7,2)[/tex]
Equate both sides.
[tex]3x=7[/tex]
[tex]x=\frac{7}{3}[/tex]
[tex]3y=2[/tex]
[tex]y=\frac{2}{3}[/tex]
Therefore the coordinates of preimage are [tex](\frac{7}{3},\frac{2}{3})[/tex].
