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What is the image of (3,-6) after a dilation by a scale factor of 4 centered at the origin?

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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).

User Jaeheung
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