Consider the points A3,4 and B7,13. If P is a point on the line y=x such that PA+PB is minimum, then the coordinates of P are

Consider a point A' the image of A in y=x. Therefore, the coordinates of A' are 4,3.Notice that A and B lies on the same side with respect to y=x. Then PA=PB' is minimum, i,e., if P,A' B are collinear. Now, the equation of A'B is y−3=13−37−4x−4or 3y−10x+31=0