Question

Find the image of the point $(2,1)$ with respect to the line mirror $x+y-5=0$.

Answer 1

Image of the point (2,1) must lie on the perpendicular from (2,1) on x+y-5=0 and at equal distance as of (2,1) from the mirror ..............1

Equation of perpendicular from (2,1) on given mirror , x-y-1=0 ................2

Let us assume coordinate of image to be (h,h-1) (Using 1 and 2)

Now midpoint of (2,1) and (h,h-1) must lie on mirror(Using 1) i.e should satisfy equation of mirror , which gives h=4 .

Thus coordinate of image is (4,3)