1.

Find area of the triangle with vertices at the point given in each of the following : (i) (1,0), (6,0), (4,3) (ii) (2,7), (1,1), (10,8)

Answer» (i) Area of `Delta`
`=1/2|{:(1,0,1),(6,0,1),(4,3,1):}|`
`=1/2|1(0-3)-0(6-4)+1(18-0)|`
`=1/2(-3-0+18)=15/2"sq.units"`
(ii) Area of triangle `=1/2|{:(2,7,1),(1,1,1),(10,8,1):}|`
`=1/2|{:(2,7,1),(1,1,1),(10,8,1):}|" "({:(R_(1)toR_(1)-R_(2)),(R_(2)toR_(2)-R_(3)):})`
`1/2(-7+54)" "("Expanding along"C_(3))`
=23.5 sq.units
(iii) `"Area of "Delta=1/2|{:(-2,-3,1),(3,2,1),(-1,-8,1):}|`
`=1/2|-2(2+8)+3(3+1)+1(-24+2)|`
`=1/2|-20+12-22|=15`sq.units


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