A triangle with vertices at A(20.-30), B(10, -15), and C(5,-20) has been dilated with a center of dilation at the origin. The image ofB, point B', has the coordinates (2, -3). What is the scale factor of the dilation?10510​

 To find the scale factor of the dilation, we need to compare the coordinates of point B before and after the dilation. We are given that before the dilation, point B has the coordinates (10, -15), and after the dilation, the image of point B, called B', has the coordinates (2, -3).

We can determine the scale factor by taking the ratio of the coordinates of B' to the coordinates of B. We can do this for either the x-coordinates or the y-coordinates, as the scale factor should be consistent for both.

Using the x-coordinates, the scale factor k can be found using the following equation:

k = B'x / Bx

Substituting the values we have:

k = 2 / 10

k = 0.2

Therefore, the scale factor of the dilation is 0.2.

Extra: A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The scale factor determines how much larger or smaller the image will be compared to the original figure. If the scale factor is greater than 1, the image will be an enlargement. If the scale factor is between 0 and 1, as it is in this case, the image will be a reduction.

In this problem, we found the scale factor by taking the ratio of the coordinates of a point after dilation (B') to its coordinates before dilation (B). When the dilation center is at the origin (0,0), this method works because all points are dilated outwards or inwards from the origin by the same proportion, which is the scale factor. If the dilation center were not at the origin, finding the scale factor would require a different approach that takes into account the relative positions of the points to the center of dilation.