What is the image of left parenthesis, 3, comma, minus, 7, right parenthesis(3,−7) after a reflection over the line y, equals, xy=x?

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.

What is the image of (3, -7) after a reflection over the line y = x?

Find the image of the point (3, -7) after reflecting it over the line y = x. This problem involves coordinate geometry and the reflection theorem, suitable for students in Grades 8-10. Step-by-step solution provided.

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