Triangle ABC is dilated by a scale factor of 
 
.  If A(52, -2), what are the coordinates of A'?

To find the coordinates of \( A' \) after a dilation, we need two pieces of information:

1. The coordinates of the original point \( A \), which are \( (52, -2) \).
2. The scale factor of the dilation, which wasn't provided in your question. 

If we call the scale factor \( k \), the formula for the new coordinates \( (x', y') \) after dilation is:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

Given that:
\[
A = (52, -2)
\]
the coordinates of \( A' \) would be:
\[
A' = (k \cdot 52, k \cdot (-2)) = (52k, -2k)
\]

Please provide the scale factor \( k \) so I can calculate the exact coordinates of \( A' \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the general formula for dilating any point on a plane?
2. How does the center of dilation affect the coordinates of the dilated point?
3. Can dilation change the shape of a figure, or does it only change the size?
4. What happens to the coordinates of a point if the scale factor is less than 1?
5. How would you dilate a point if the center of dilation is not at the origin?

**Tip:** When dealing with dilation, always note the center of dilation; if it is not at the origin, the transformation rules will change.

Triangle ABC is dilated by a scale factor of . If A(52, -2), what are the coordinates of A'?

Learn how to find the coordinates of point A' after dilating point A(52, -2) by a scale factor. Understand the key geometric transformation concepts and formulas related to dilation, suitable for Grades 8-10.

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