Question

A triangle with vertices at A0, 0), 80, 4), and C6, 0) Is dilated to yield a triangle with vertices at A[0, 0), B10, 10), and C115,0). The origin is the

center of dilation. What is the scale factor of the dilation?

Answer 1

To find the scale factor, compare the corresponding coordinates of a point before and after dilation. Using point B's y-coordinates (since point B's original x-coordinate is 0), the scale factor is 10 (new y-coordinate) divided by 4 (original y-coordinate), which equals 2.5.

Step-by-step explanation:

The scale factor of a dilation can be determined by comparing the measurements of a figure before and after the dilation when the center of dilation is the origin. To find the scale factor, you can compare corresponding lengths of the two triangles. Let's take the coordinates of point B before and after the dilation: originally B(0, 4) and after dilation B'(10, 10). Since the x-coordinate and the y-coordinate both increase by the same factor, we can calculate the scale factor by taking the ratio of the new coordinates to the old ones.

For example, we can divide the new x-coordinate of B' by the original x-coordinate of B (which would be 10/0, but since division by zero is undefined, let's use the y-coordinates). So the scale factor k would be 10/4, which simplifies to 2.5. Therefore, the scale factor of the dilation is 2.5.