A dilation has center (0, 0, 0)
. Find the image of the point (−1, −2, 0)
for the scale factor of 3.
To find the image of the point (-1, -2, 0) after a dilation with a scale factor of 3 and a center at (0, 0, 0), we can use the formula for dilation in three dimensions:
(x', y', z') = (cx, cy, cz)
where (x, y, z) are the coordinates of the original point, (x', y', z') are the coordinates of the image point, and c is the scale factor.
Plugging in the values:
(x', y', z') = (3 * -1, 3 * -2, 3 * 0)
(x', y', z') = (-3, -6, 0)
Therefore, the image of the point (-1, -2, 0) after the dilation with a scale factor of 3 and center at (0, 0, 0) is (-3, -6, 0).