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

Explanation

Let`(x_(1),y_(1))` be the image of `(-sqrt2,sqrt2)` about the line `y=xtan((pi)/(8)).`
On comparing `y=x tan ((pi)/(8)) by y = x tan theta`
` therefore" " theta=(pi)/(8)`
Now, `[(,x_(1)),(,y_(1))]=[(cos2theta,sin2theta),(sin2theta,-cos2theta)][(,-sqrt2),(,sqrt2)]`
`[((1)/sqrt2,(1)/sqrt2),((1)/sqrt2,(1)/sqrt2)][(,-sqrt2),(,sqrt2)]=[(,0),(,-2)]`
On comparing `x_(1)=0 and y_(1)=-2`
therefore, the requried image is `(0,-2)`