Area of triangle whose vertices are `(a,a^2),(b,b^2),(c,c^2)` is `1/2` . and area of another triangle whose vertices are `(p,p^2),(q,q^2) and (r,r^2)` is 4, then the value of `|((1+ap)^2,(1+bp)^2,(1+cp)^2),((1+aq)^2,(1+bp)^2,(1+cq)^2),((1+ar)^2,(1+br)^2,(1+cr)^2)|` is (A) 2 (B) 4 (C) 8 (D) 16

Options

A. `2`
B. `4`
C. `8`
D. `16`

Answer

D

Explanation

`(d)` `|{:((1+ap)^(2),(1+bp)^(2),(1+cp)^(2)),((1+aq)^(2),(1+bq)^(2),(1+cq)^(2)),((1+ar)^(2),(1+br)^(2),(1+cr)^(2)):}|`
`=|{:(1,2a,a^(2)),(1,2b,b^(2)),(1,2c,c^(2)):}|xx|{:(1,p,p^(2)),(1,q,q^(2)),(1,r,r^(2)):}|`
`=2xx2Delta_(1)*2Delta_(2)`
`=8Delta_(1)Delta_(2)=8xx(1)/(2)xx4=16`