Maths / Coordinate Geometry / Distance Formula

QUESTION
 

Find the distance between A(a,b) and B(-b, a).

OPTIONS
A. 

large 2(a^{2}+b^{2});units

B. 

large sqrt{2(a^{2}+b^{2})};units

C. 

large sqrt{2(a^{2}-b^{2})};units

D. 

large sqrt{2(2a^{2}+b^{2})};units

Right Option : B

EXPLANATION
Explain TypeExplanation Content
Text

Here     large x_{1}=a,         large x_{2}=-b,     large y_{1}=b,    large y_{2}=a,

We know that large AB^{2}=(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} large =(-b-a)^{2}+(a-b)^{2} large =(b+a)^{2}+(a-b^{2})=2(a^{2}+b^{2})                                                                         large left [ because (x-y)^{2}+(x+y)^{2}=2(x^{2}+y^{2}) right ]

large Rightarrow ;;;AB=sqrt{2(a^{2}+b^{2})};units

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