Question

Given the points F(16, 8) and a dilation centered at the origin that maps the point (3, 6) to the point (5/4, 5/2), what is the scale factor of the dilation?

Answer 1

The scale factor of the dilation is 5/12.

Step-by-step explanation:

The scale factor of a dilation is a measure of how much the figure is being scaled up or down. To find the scale factor, we can use the formula:

scale factor = (image coordinate - origin coordinate) / (pre-image coordinate - origin coordinate)

Given the points F(16, 8) and a dilation centered at the origin that maps the point (3, 6) to the point (5/4, 5/2), we can substitute the coordinates into the formula:

scale factor = ((5/4, 5/2) - (0, 0)) / ((3, 6) - (0, 0))

scale factor = (5/4, 5/2) / (3, 6)

Since scaling is proportional, we can simplify the fraction:

scale factor = (5/4) / 3

Thus, the scale factor of the dilation is 5/12.