To reflect the point $(3, -7)$ over the line $y = x$, you swap the x- and y-coordinates of the point.

The coordinates of the reflected point will be: $(-7, 3)$

Thus, the image of $(3, -7)$ after a reflection over the line $y = x$ is $(-7, 3)$.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. What is the image of $(-4, 5)$ after a reflection over $y = x$?
2. How do you reflect a point over the line $y = -x$?
3. What happens to the point $(0, 0)$ when reflected over any line?
4. If you reflect $(2, 3)$ over $y = x$ and then reflect the result over the x-axis, what are the final coordinates?
5. How would you find the reflection of a point over a line like $y = 2x + 1$?

Tip: When reflecting a point over the line $y = x$, always swap the x- and y-coordinates.