Question

What would be the scale factor if A (4, 6) were dilated to A' (2, 3)?(1 point)

Answer 1

To determine the scale factor for the dilation from point A (4, 6) to point A' (2, 3), you can use the formula for dilation, which relates the coordinates of the original point and the dilated point as follows:

Scale Factor \( k = \frac{\text{Coordinates of } A'}{\text{Coordinates of } A} \)

We can calculate the scale factor for both the x and y coordinates:

1. For the x-coordinates:
\[
k_x = \frac{x'}{x} = \frac{2}{4} = \frac{1}{2}
\]

2. For the y-coordinates:
\[
k_y = \frac{y'}{y} = \frac{3}{6} = \frac{1}{2}
\]

Since both scale factors are the same, the overall scale factor \( k \) is:
\[
k = \frac{1}{2}
\]

Thus, the scale factor is \( \frac{1}{2} \).