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

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

View Contents
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)
Self Learning
Testimonials
PARENT RESPONSE c/o Prisha Gupta C/o ABHYAS Academy
8th
Being a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.

#### Other Testimonials

Courses We Offer
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)