Plot the image of point   under a dilation about point   with a scale factor of  .  Related content

To assist you effectively, I would need specific details about the point, the center of dilation, and the scale factor. However, I can provide you with the general steps to perform a dilation transformation.

1. Break Down the Problem

• Identify the coordinates of the original point, the center of dilation, and the scale factor.
• Dilation involves expanding or contracting the original point based on the distance from the center of dilation.

2. Relevant Concepts

• The formula for dilation about a point $P(c, d)$ with a scale factor $k$ is given by: $(x', y') = (c + k(x - c), d + k(y - d))$ where $(x, y)$ are the coordinates of the original point, and $(x', y')$ will be the coordinates of the dilated point.

3. Analysis and Detail

• Substitute the coordinates of the original point into the dilation formula.
• Compute the new coordinates meticulously.
  • For example, if the point is $(x, y)$, the center of dilation is $(c, d)$, and the scale factor is $k$: $x' = c + k(x - c)$ $y' = d + k(y - d)$
• Carry out any calculations needed to determine $x'$ and $y'$.

4. Verify and Summarize

• Double-check the calculations by ensuring all additions and multiplications are accurate.
• Summarize the findings by stating the coordinates of the dilated point.

Final Answer

Provide the final coordinates of the dilated point as $(x', y')$.

If you provide the specific numbers, I can perform the calculations and give you the exact coordinates of the dilated point.