Find the image of the point `(-sqrt2,sqrt2)` by the line mirror` y=x tan ((pi)/(8)).`

Explanation

To find the image of the point \((- \sqrt{2}, \sqrt{2})\) by the line mirror \(y = x \tan\left(\frac{\pi}{8}\right)\), we can follow these steps:

### Step 1: Determine the slope of the line
The line \(y = x \tan\left(\frac{\pi}{8}\right)\) has a slope \(m = \tan\left(\frac{\pi}{8}\right)\).

Using the identity for tangent:
\[
\tan\left(\frac{\pi}{8}\right) = \frac{\sqrt{2} - 1}{\sqrt{2} + 1}
...