उस त्रिभुज का क्षेत्रफल क्या है, जिसके शीर्ष - बिन्दु `(x_(1), 1/(x_(1))), (x_(2), 1/(x_(2))), (x_(3), 1/(x_(3)))` हैं ?

Options

A. `|(x_(1)-x_(2))(x_(2)-x_(3)) (x_(3) - x_(1))|`
B. 0
C. `|((x_(1)-x_(2))(x_(2)-x_(3))(x_(3)-x_(1)))/(x_(1)x_(2)x_(3))|`
D. `|((x_(1)-x_(2))(x_(2)-x_(3)) (x_(3) - x_(1)))/(2x_(1)x_(2)x_(3))|`

Explanation

दिए गए बिन्दु `A(x_(1),1/(x1)),B(x_(2),1/(x_(2)))` तथा `C(x_(2), 1/(x_(3)))` है
`:. DeltaABC` का क्षेत्रफल
`A = 1/2|{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|`
`= 1/2 |{:(x_(1),1/(x_(1)),1),(x_(2),1/(x_(2)),1),(x_(3),1/(x_(3)),1):}|=1/2|{:(x_(1),1/(x_(1)),1),(x_(2),1/(x_(2)),1),(x_(3),1/(x_(3)),1):}|`
`rArr1/(2x_(1)x_(2)x_(3))|{:(x_(1)^(2),1,x_(1)),(x_(2)^(2),1,x_(2)),(x_(3)^(3),1,x_(3)):}|`
`= |((x_(1)-x_(2))(x_(2)-x_(3))(x_(3)-x_(1)))/(2x_(1)x_(2),x_(3))|`