If the line 4x−5y+41=0 is the perpendicular bisector of the line segment joining the points A1,1 and B  .The image of B in  x-axis is a,b  then the numerical value of a+b  is

The point B is the image of A1,1 with respect to the line 4x−5y+41=0If h,k is the image of the point x1,y1 with respect to the line ax+by+c=0 then h−x1a=k−y1b=−2ax1+by1+ca2+b2Hence,  h−14=k−1−5=−24−5+4142+−52           Simplify  h−14=k−1−5=−8041           Hence,h−14=−8041h=−32041+1=−320+4141=−27941Ik−1−5=−8041k=40041+1=44141Hence,h,k=−27941,44141The image of Bh,k in x-axis is  a,b=h,−ka+b=h−k=−441−27941=−72041=−17.56Therefore,  a+b=−17.56