Final answer:
The image of the point (-4, 9) after a dilation by a scale factor of 3 centered at the origin is (-12, 27).
Step-by-step explanation:
The image of a point after a dilation by a scale factor can be found by multiplying the original coordinates by the scale factor. In the case of the original point (-4, 9) and a dilation by a scale factor of 3 centered at the origin, you simply multiply both the x-coordinate and the y-coordinate by 3.
To find the new coordinates:
x' = x × scale factor = -4 × 3 = -12
y' = y × scale factor = 9 × 3 = 27
Therefore, the image of (-4, 9) after the dilation would be (-12, 27).