Question

find the distance between the points A and B if A(a+b,b-a）,B（a-b,a+b

Answer 1

Distace between the points (x, y) and  (a+b, b-a) & (a-b, a+b) is equal  ⇒ √{[x - (a + b)]2 + [y - (b -a)]2} = √{x - (a - b)]2 + [y - (a + b)]2} ⇒ x2 + (a + b)2 - 2x(a + b) + y2 + (b - a)2 - 2y(b - a) = x2 + (a - b)2 - 2x(a - b) + y2 + (a + b)2 - 2y(a + b) ⇒ -2ax - 2bx - 2by + 2ay = - 2ax + 2bx - 2ay - 2by ⇒ ay - bx = bx - ay ⇒ 2ay = 2bx ⇒ bx = ay Hence proved.
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Answer 2

Distance formula

√(x₂-x₁) + (y₂-y₁)

√(a-b-a-b)² + (a+b-b+a)²

√(-2b)²+ (2a)²

√4b²+ 4a²

√4(a²+b²)

2√(a²+b²)