If the image of the point (3,8) in the line x+3 y=7 is ( , ) , then + =

Step-by-step solution

Let line AB be x +3 y =7 and point P be (3,8) . Let Q (h, k) be the image of point P(3,8) in the line x+3 y=7 . Since line AB is a mirror. (1) Point P & Q are at equal distance from line AB i.e. P R=Q R i.e. R is the mid-point of P Q . (2) Image is formed perpendicular to mirror i.e. line P Q is perpendicular to line AB . Since R is the midpoint of PQ . Mid point of PQ joining (3,8) and ( h , k ) is ( h +3 2 , h +8 2 ) Coordinate of point R = ( h +3 2 , h +8 2 ) Since point R lies on the line AB . Therefore, ( 3+ h