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

If the segment joining the points \[(a,b)\] and \[(c,d)\] subtends a right angle at the origin, then:

A) \[ac-bd=0\]

B) \[ac+bd=0\]

C) \[ab+cd=0\]

D) \[ab-cd=0\]

Correct Answer: B

Solution :

[b] Let \[A(a,b),\,\,\,B(c,d),\,\,O(0,0)\]

\[\therefore \,\,\,\,\angle AOB=90{}^\circ \,\,\,\,\Rightarrow \,\,\,A{{B}^{2}}=A{{O}^{2}}+B{{O}^{2}}\]

\[\therefore \,\,\,{{(c-a)}^{2}}+{{(d-b)}^{2}}={{a}^{2}}+{{b}^{2}}+{{c}^{2}}+{{d}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,ac+bd=0\]