Question

Under a dilation centered at the origin, the vertex, (3, −5), of a polygon is moved to the point (−15, 25) .

What is the scale factor of the dilation?

Answer 1

-5

Explanation:

To find the scale factor of the dilation, we can compare the (x, y) coordinates of the original point (vertex) to the (x, y) coordinates of the image point after dilation.

Given:

• Original point: (3, -5)
• Image point after dilation: (-15, 25)

The scale factor (k) can be calculated by dividing the x-coordinate of the dilated point (image) by the x-coordinate of the original point:

`k=(-15)/(3)=-5`

In the context of a dilation centered at the origin, a negative scale factor means that the image point is on the opposite side of the origin compared to the original point.

So, a dilation of scale factor -5 means that the image point is five times farther from the origin compared to the original point, on the opposite side of the origin.