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

Which of the points\[A(1,3),\]\[B(-3,2),\] \[C(-3,2),\] and D(4,1) is nearest to the origin?

A) A

B) B

C) C

D) D

Correct Answer: A

Solution :

[a] Since distance of \[(x,y)\]from origin \[=\sqrt{{{x}^{2}}+{{y}^{2}}}\]

\[\therefore \,\,\,\,\,\,\,\,\,\,OA=\sqrt{1+9}=\sqrt{10}\]

\[OB=\sqrt{9+4}=\sqrt{13}\]

\[OC=\sqrt{9+16}=\sqrt{25}=5\]

\[OD=\sqrt{16+1}=\sqrt{17}\]

Since OA is the shortest distance.

\[\therefore \] A is nearest to the origin.