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

The distance between the points \[(a,b)\] and \[(-a,-b)\] is: (CBSE 2019)

A) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\] units

B) \[\frac{1}{2}\sqrt{{{a}^{2}}+{{b}^{2}}}\] units

C) \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\] units

D) \[\sqrt{a+b}\] units

Correct Answer: C

Solution :

[c] Distance between \[(a,b)\]and \[(-a,-b)\] is given by

\[d=\sqrt{{{(-a-a)}^{2}}+{{(-b-b)}^{2}}}\]

\[=\sqrt{{{(-2a)}^{2}}+{{(-2b)}^{2}}}=\sqrt{4{{a}^{2}}+4{{b}^{2}}}=2\sqrt{{{a}^{2}}+{{b}^{2}}}\]units.