To determine the reflection of the point (1, 13) across the line \( y = x \) and identify in which quadrant it lies, we first understand how reflection across the line \( y = x \) works.
When a point \( (a, b) \) is reflected across the line \( y = x \), the coordinates of the reflected point become \( (b, a) \).
For the point \( (1, 13) \):
- The reflection across the line \( y = x \) gives us the point \( (13, 1) \).
Now we need to identify the quadrant in which the point \( (13, 1) \) lies.
- The x-coordinate is 13, which is positive.
- The y-coordinate is 1, which is also positive.
Since both coordinates are positive, the point \( (13, 1) \) lies in the first quadrant of the coordinate plane.
Thus, the answer is that the reflected point is located in the first quadrant.
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