यदि बिंदु `(p_(1),q_(1)), (p_(2),q_(2))` तथा `(p_(1)-p_(2),q_(1)-q_(2))` सरिख हो तो सिद्ध कीजिये कि

Explanation

यहाँ `x_(1)=p_(1),x_(2)=p_(2),x_(3)=p_(1)-p_(2)`
`y_(1)=q_(1),y_(2)=q_(2),y_(3)=q_(1)-q_(2)`
सरेख होने का प्रतिबन्ध है:
`x_(1)(y_(2)-y_(3))+x_(2)(y_(3)-y_(1))+x_(3)(y_(1)-y_(2))=0`
`p_(1)(q_(2)-q_(1)+q_(2))+p_(2)(q_(1)-q_(2))=0`
`2p_(1)q_(2)-p_(1)q_(1)-p_(2)q_(1)-p_(1)q_(2)-p_(2)q_(1)+p_(2)q_(2)=0`
`2p_(1)q_(2)-p_(1)q_(2)-p_(1)q_(1)-p_(2)q_(2)+p_(2)q_(1)=0`
`p_(1)q_(2)-p_(2)q_(1)=0`
`p_(1)q_(2)=p_(2)q_(1)` इति सिद्धम