If the line 4x−5y+41=0 is the perpendicular bisector of the line segment joining the  points A(1,1) 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 A(1,1) with respect to the line 4x−5y+41=0 If (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+−52Simplify   h−14=k−1−5=−8041          Hence,    h−14=−8041h=−32041+1=−320+4141=−27941       k−1−5=−8041k=40041+1=44141 Hence ,(h,k)=−27941,44141 The image of B(h,k) with respect to x− axis is (h,−k) = (a,b)a+b=h−k=−441−27941=−72041=−17.56 Therefore, a+b=−17.56