Line segment AB is dilated to create line segment A'B' using point Q as the center of dilation.

Question

Point Q is the center of dilation. Line segment A B is dilated to create line segment A prime B prime. The length of Q A is 1.25 and the length of A A prime is 1.25.

What is the scale factor?

1
1.25
2
2.5

Answer 1

To determine the scale factor of the dilation, we can use the formula related to the lengths involved in the dilation:

\[ \text{Scale Factor} = \frac{\text{Length of } QA'}{\text{Length of } QA} \]

From the problem, we know:

• The length of \( QA \) is \( 1.25 \).
• The length of \( AA' \) is also \( 1.25 \).

First, we find the length of \( QA' \). Since \( Q \) is the center of dilation, we have:

\[ QA' = QA + AA' = 1.25 + 1.25 = 2.5 \]

Now we can calculate the scale factor:

\[ \text{Scale Factor} = \frac{QA'}{QA} = \frac{2.5}{1.25} = 2 \]

Thus, the scale factor is 2.