Question

Find the scale factor that was used in the dilation shown.


S (6,4)

'S (9,6)

Answer 1

To find the scale factor of the dilation from point S (6, 4) to point S' (9, 6), we can use the formula for the scale factor \( k \):

\[
k = \frac{\text{new coordinate}}{\text{original coordinate}}
\]

Let's calculate the scale factor for the x-coordinates and y-coordinates separately.

1. For the x-coordinates:

\[
k_x = \frac{9}{6} = \frac{3}{2} = 1.5
\]

2. For the y-coordinates:

\[
k_y = \frac{6}{4} = \frac{3}{2} = 1.5
\]

Since both calculations give us the same scale factor, the scale factor used in the dilation is:

\[
\boxed{1.5}
\]