Question

What is the image of left parenthesis, 7, comma, 8, right parenthesis(7,8) after a reflection over the line y, equals, minus, xy=−x?

Answer 1

To find the image of the point \((7, 8)\) after a reflection over the line \(y = -x\), we will follow the process of reflecting a point across this line.

The general procedure for reflecting the point \((x, y)\) across the line \(y = -x\) is to swap the coordinates and change their signs. Specifically, the point \((x, y)\) transforms as follows:

\[
(x, y) \rightarrow (-y, -x)
\]

Now, applying this to the point \((7, 8)\):

1. Swap the coordinates:
- Original: \((7, 8)\)
- After swapping: \((8, 7)\)

2. Change their signs:
- After changing signs: \((-8, -7)\)

Thus, the image of the point \((7, 8)\) after a reflection over the line \(y = -x\) is:

\[
\boxed{(-8, -7)}
\]