Point C is the center of dilation. Line segment B A is dilated to create line segment B prime A prime. The length of C A is 4. The length of A A prime is 16.

Question

What is the scale factor of the dilation of line segment BA?

One-fifth
One-fourth
4
5

Answer 1

To find the scale factor of the dilation, we can use the relationship between the lengths before and after dilation.

The length of the original segment \(CA\) is given as 4, and the length of the new segment \(AA'\) is given as 16.

The scale factor of the dilation (\(k\)) can be calculated using the formula:

\[ k = \frac{\text{length of the new segment}}{\text{length of the original segment}} = \frac{AA'}{CA} \]

Substituting the values:

\[ k = \frac{16}{4} = 4 \]

Therefore, the scale factor of the dilation of line segment \(BA\) is \( \boxed{4} \).