Answer: The scale factor of the dilation is [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given: The image of (6, 9) under a dilation is (4, 6).
In dilation, the scale factor 'k' is the ratio of the coordinate of image to the coordinate of pre-image.
Taking the x coordinates of both image and preimage, we get
[tex]k=\frac{\text{image x coordinate}}{\text{pre-image x coordinate}}\\\\\Rightarrow\ k=\frac{4}{6}\\\\\Rightarrow\ k=\frac{2}{3}[/tex]
Hence, the scale factor of the dilation is [tex]\frac{2}{3}[/tex]
