1.

Find the area of a rhombups if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.

Answer»

Solution :Let A(3, 0) , B(4, 5), C(-1, 4) and D(-2, -1) be the vertices of the rhombus ABCD.
`therefore"""DIAGONAL, "AC=SQRT((-1-3)^(2)+(4-0)^(2))`
`""[because "distance "=sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2))]`
`""=sqrt((-4)^(2)+4^(2))=sqrt(16+16)=sqrt(32)=4sqrt(2)`
`"""Diagonal, "BD=sqrt((-2-4)^(2)+(-1-5)^(2))=sqrt((-6)^(2)+(-6)^(2))`
`""=sqrt(36+36)=sqrt(72)=6sqrt(2)`
`therefore` Area of the rhombus ABCD `=(1)/(2)xxACxxBD=(1)/(2)xx4sqrt(2)xx6sqrt(2)`
`""=2xx6xxsqrt(2)xxsqrt(2)=12xx2=24` SQUARE units


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