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The question in the image asks for the coordinates of the image of point \( S(6, -2) \) after two transformations: 
1. A dilation with a scale factor of \(-2\) centered at \( (0,0) \).
2. A reflection across the line \( y = -x \).

### Step 1: Dilation with scale factor \(-2\)
The formula for dilation centered at the origin with scale factor \( k \) is:
\[
(x', y') = (k \cdot x, k \cdot y)
\]
For the point \( S(6, -2) \) and \( k = -2 \), we calculate:
\[
x' = -2 \cdot 6 = -12
\]
\[
y' = -2 \cdot (-2) = 4
\]
Thus, after dilation, the coordinates of the point are \( (-12, 4) \).

### Step 2: Reflection across the line \( y = -x \)
The formula for reflecting a point \( (x, y) \) across the line \( y = -x \) is:
\[
(x'', y'') = (-y, -x)
\]
For the point \( (-12, 4) \), we calculate:
\[
x'' = -4
\]
\[
y'' = 12
\]
Thus, after reflection, the coordinates of the point are \( (-4, 12) \).

### Final Answer:
The coordinates of the image of point \( S(6, -2) \) after the given transformations are \( (-4, 12) \).

Would you like further details or have any questions?

Here are five related questions for further practice:
1. How would the coordinates change if the scale factor was \(+2\) instead of \(-2\)?
2. What is the formula for reflecting a point across the \( y \)-axis?
3. How do you reflect a point across the line \( y = x \)?
4. What happens to a point’s coordinates after a dilation with a scale factor of \(1\)?
5. How do you perform a translation of a point by adding specific values to \(x\) and \(y\)?

**Tip:** When performing a reflection across the line \( y = -x \), always switch and negate the coordinates of the point.

Koordinat bayangan titik S (6, -2) yang didilatasi pada pusat (0,0) dengan faktor skala -2 kemudian dilanjutkan dengan pencerminan terhadap garis y = -x.

Solve the problem of finding the coordinates of point S (6, -2) after a dilation with a scale factor of -2 and a reflection across the line y = -x. Learn key concepts in coordinate geometry, including dilation and reflection transformations.

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