Question

What is the scale factor of this dilation?
Triangle X Y Z. Side X Y is 10, Z Y is 12, Z X is 8. Triangle X prime Y prime Z prime. Side X prime Y prime is 7.5, Z prime Y prime is 9, Z prime X prime is 6.
One-half
Two-thirds
Three-fourths
Three-halves

Answer 1

To find the scale factor of the dilation between triangle XYZ and triangle X'Y'Z', we can compare the corresponding sides of the triangles.

The sides of triangle XYZ are:
- XY = 10
- ZY = 12
- ZX = 8

The sides of triangle X'Y'Z' are:
- X'Y' = 7.5
- Z'Y' = 9
- Z'X' = 6

To find the scale factor, we can compare the corresponding sides. Let's take the first side comparison, XY and X'Y':

\[
\text{Scale factor} = \frac{\text{Side of triangle X'Y'Z'}}{\text{Side of triangle XYZ}}
\]

Calculating for side XY and X'Y':
\[
\text{Scale factor} = \frac{7.5}{10} = \frac{3}{4}
\]

Now, let's check the other sides for confirmation:

For sides ZY and Z'Y':
\[
\text{Scale factor} = \frac{9}{12} = \frac{3}{4}
\]

For sides ZX and Z'X':
\[
\text{Scale factor} = \frac{6}{8} = \frac{3}{4}
\]

Since all calculations give the same scale factor of \(\frac{3}{4}\), we can conclude that the scale factor of the dilation is:

**Three-fourths**