10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

If A and B are the points \[(-6,7)\] and \[(-1,-5)\] respectively, then the distance \[2AB\] is equal to: (CBSE 2011)

A) \[13\]

B) \[26\]

C) \[169\]

D) \[238\]

Correct Answer: B

Solution :

[b] \[A(-6,7),\,\,B(-1,-5)\]

Let\[{{x}_{1}}=-6,\,\,{{y}_{1}}=7\]

\[{{x}_{2}}=-1,\,\,{{y}_{2}}=-5\]

Distance, \[AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{3}}}\]

\[=\sqrt{{{(-1+6)}^{2}}+{{(-5-7)}^{2}}}\]

\[=\sqrt{{{5}^{2}}+{{(-12)}^{2}}}=\sqrt{25+144}=\sqrt{169}=13\]

\[2AB=2\times 13=26\]