Question

Find the distance between the following pairs of points :- (a+b,a-b), (b-a, a+b)​

Answer 1

Answer:

2√ [a² + b²]

Step-by-step explanation:

Consider those two points as A(x₁, y₁) & B(x₂, y₂)

Given that A = (a+b,a-b) & B = (b-a, a+b)​

We know that the distance between two points is √ [(x₂ - x₁)² + (y₂ - y₁)²]

=> √ [(b - a - a - b)² + (a + b + b - a)²]

=> √ [(-2a)² + (2b)²]

=> √ [4a² + 4b²]

=> √ 4[a² + b²]

=> 2√ [a² + b²]

Answer 2

${\mathcal\red{\underline {\underline{Answer:}}}}$

$\bold\blue{{2\sqrt{({a}^{2}+{b}^{2})}}}$

${\mathcal\red{\underline {\underline{Step-by-step\:explanation:}}}}$

Here,

$(a + b,a - b) = (x1 ,y1) \\ (b - a,a + b) = (x2,y2) \\ \\ As, \: we \: know \: that, \\ distance \: between \: pairs = \sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} } \\ \\ ∴The \: distances \: between \: the \: following \: pairs \: of \: point \\ = \sqrt{ {(b - a - b - a)}^{2} + {(a + b - a + b)}^{2} } \\ = \sqrt{( - 2a)^{2} + ( {2b})^{2} } \\ = \sqrt{4 {a}^{2} + 4 {b}^{2} } \\ = \sqrt{4( {a}^{2} + {b}^{2}) } \\ = \sqrt{4} \times \sqrt{( {a}^{2} + {b}^{2}) } \\ = 2 \sqrt{( {a}^{2} + {b}^{2} )}$

$\bold\green{\sf{\boxed{Hence,\:the\:distance\:between\:the\:following\:pairs\:of\:points\:is\:2\sqrt{({a}^{2}+{b}^{2})}}}}$

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