The problem asks you to determine the scale factor of dilation based on the transformation shown in the image. The original points are labeled as $A$ and $B$, and the transformed points are labeled as $A_1'$ and $B_1'$.

Analysis:

1. Point $A$ is located at (1, 1).
2. Point $B$ is located at (5, 1).
3. Dilated Point $A_1'$ is located at (1, 2).
4. Dilated Point $B_1'$ is located at (5, 2).

The dilation appears to be vertical, as only the y-coordinates have changed. The y-coordinates of $A$ and $B$ are multiplied by a factor to get the y-coordinates of $A_1'$ and $B_1'$.

Calculating the Scale Factor:

For point $A$:

• Original y-coordinate: 1
• Transformed y-coordinate: 2

Scale factor = $\frac{\text{New y-coordinate}}{\text{Original y-coordinate}} = \frac{2}{1} = 2$.

Conclusion:

The scale factor of the dilation is 2.

Would you like further details or explanations on this topic? Here are some related questions:

1. How do you determine the scale factor of a dilation in general?
2. What are the effects of a scale factor greater than 1 versus less than 1?
3. How does dilation affect the coordinates of a point?
4. Can dilation occur in both x and y directions simultaneously?
5. What happens to shapes under dilation with a scale factor of 0?

Tip: When working with dilations, always compare corresponding coordinates to find the scale factor!