The correct option is C 2√2b
Distance between points (x1,y1) and (x2,y2) = √(x2−x1)2+(y2−y1)2
Let's name the points as A(a + b, b + c) and B(a - b, c - b) .
AB = √(x2−x1)2+(y2−y1)2
⇒AB2= (a+b−(a−b))2+(b+c−(c−b))2
⇒AB2=4b2+4b2=8b2
⇒AB=2√2b
Therefore, the distance between points (a + b, b + c) and (a – b, c – b) is 2√2b units.