A dilation has center (0, 0, 0). Find the image of the point (–2, –3, 0) for the scale factor of 3.
To find the image of the point, we need to apply the dilation formula:
(x', y', z') = k(x, y, z)
where (x, y, z) is the original point, k is the scale factor, and (x', y', z') is the image point.
In this case, the original point is (-2, -3, 0) and the scale factor is 3. So, we have:
(x', y', z') = 3(-2, -3, 0)
= (-6, -9, 0)
Therefore, the image of the point (-2, -3, 0) under a dilation with center (0, 0, 0) and a scale factor of 3 is (-6, -9, 0).