What is the scale factor of a dilation centered at the origin that maps the point (12, -8) to the point (-7.2, 4.8)? Please show work as it will help me better understand, thanks so much!

12 * s = -7.2 ... s = -.6

-.6 * -8 = 4.8

To find the scale factor of a dilation, we can use the formula:

scale factor = distance of image / distance of pre-image

In this case, the pre-image is the point (12, -8) and the image is the point (-7.2, 4.8). We need to find the distance between these two points.

The distance between two points can be found using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's plug in the coordinates of the pre-image (x1, y1) = (12, -8) and the image (x2, y2) = (-7.2, 4.8) into the distance formula:

distance = sqrt((-7.2 - 12)^2 + (4.8 - (-8))^2)

distance = sqrt((-19.2)^2 + (12.8)^2)

distance = sqrt(368.64 + 163.84)

distance = sqrt(532.48)

distance ≈ 23.09

Now that we have the distance of the image, we can find the distance of the pre-image. Since the dilation is centered at the origin (0,0), the distance of the pre-image would be the same as the distance between the origin and the pre-image, which is also equal to the distance of the image.

Therefore, the scale factor is:

scale factor = 23.09 / 23.09

scale factor = 1

So, the scale factor of the dilation centered at the origin that maps the point (12, -8) to the point (-7.2, 4.8) is 1.