Question

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.

Answer 1

The scale factor, r, is found relating two proportional sides, as follows:

`\begin{gathered} 40=r\cdot8 \\ (40)/(8)=r \\ 5=r \end{gathered}`

Therefore, the relation between sides z and 10 is:

`\begin{gathered} z=r\cdot10 \\ z=5\cdot10 \\ z=50 \end{gathered}`

And the value of y is:

10 + y = z

10 + y = 50

y = 50 - 10

y = 40

Finally, the value of x is:

`\begin{gathered} x=6\cdot r \\ x=6\cdot5 \\ x=30 \end{gathered}`