The following describes a dilation with center O and image of the segment of length 6 in bold. Find the scale factor and the lengths designated by x and y.

The scale factor, r, is found relating two proportional sides, as follows:
[tex]\begin{gathered} 40=r\cdot8 \\ \frac{40}{8}=r \\ 5=r \end{gathered}[/tex]Therefore, the relation between sides z and 10 is:
[tex]\begin{gathered} z=r\cdot10 \\ z=5\cdot10 \\ z=50 \end{gathered}[/tex]And the value of y is:
10 + y = z
10 + y = 50
y = 50 - 10
y = 40
Finally, the value of x is:
[tex]\begin{gathered} x=6\cdot r \\ x=6\cdot5 \\ x=30 \end{gathered}[/tex]