Question

What is the scale factor of the dilation centered at the origin if G(-9,6) becomes G'(3,-2)?

Answer 1

The scale factor of the dilation centered at the origin is -1/3, as we found by comparing the coordinates of G(-9,6) and G'(3,-2).

Step-by-step explanation:

To find the scale factor of the dilation, we'll compare the coordinates of the pre-image point G(-9,6) to the coordinates of the image point G'(3,-2). Since the dilation is centered at the origin, we can simply divide the coordinates of the image by the coordinates of the pre-image.

For the x-coordinates: The scale factor for the x-coordinate is 3 / -9 = -1/3. For the y-coordinates: The scale factor for the y-coordinate is -2 / 6 = -1/3.

We observe that both the x-coordinate and the y-coordinate of G' are -1/3 the corresponding coordinates of G, which means the scale factor is -1/3.