Final answer:
The image of the point (3,-6) after a dilation by a scale factor of 4 is (12, -24).
Step-by-step explanation:
To find the image of the point (3,-6) after dilation by a scale factor of 4 centred at the origin, you need to multiply both coordinates of the point by the scale factor. The coordinate transformation for dilation concerning the origin is:
x' = k × x
y' = k × y
Where (x, y) is the original point, (x', y') is the transformed point, and k is the scale factor. In this case, the scale factor is 4.
Therefore, the transformed coordinates are:
x' = 4 × 3 = 12
y' = 4 × (-6) = -24
The image of the point (3,-6) after the dilation is (12, -24).