Question

Determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin.
Given
A (2,2)
B (1,1)
A' (10,10)
B' (5,5)

Answer 1

To determine the scale factor used in the dilation of line \( AB \) with center point at the origin, we can use the coordinates of the original points \( A \) and \( B \) and their dilated counterparts \( A' \) and \( B' \).

The coordinates are given as follows:
- Original point \( A(2, 2) \) dilates to \( A'(10, 10) \)
- Original point \( B(1, 1) \) dilates to \( B'(5, 5) \)

The scale factor \( k \) for a dilation can be calculated by the formula:

\[
k = \frac{ \text{coordinate of dilated point} }{ \text{coordinate of original point} }
\]

Let's calculate the scale factor for point \( A \):

\[
k = \frac{10}{2} = 5
\]

Now, let's calculate the scale factor for point \( B \):

\[
k = \frac{5}{1} = 5
\]

Both points give us the same scale factor. Therefore, the scale factor used in the dilation of line segment \( AB \) is:

\[
\boxed{5}
\]