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 switch the coordinates of the point. This is because the reflection over \(y = x\) interchanges the \(x\)- and \(y\)-coordinates of the point.

Given the point \((3, -7)\):
- After reflection over \(y = x\), the coordinates are reversed.

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

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you reflect a point over the line \(y = -x\)?
2. What happens when you reflect a point over the \(x\)-axis or \(y\)-axis?
3. How can you determine the distance of a point from a line before and after reflection?
4. What is the image of the point \((-7, 3)\) after reflecting over \(y = x\) again?
5. How do transformations like reflections affect the orientation of geometric shapes?

**Tip:** To reflect over \(y = x\), simply swap the \(x\)- and \(y\)-coordinates. For \(y = -x\), swap and negate both.

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 explores key geometry concepts related to reflections and coordinate transformations, suitable for students in Grades 8-10.

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