First slide

Cartesian plane

Question

The area of the quadrilateral whose vertices are $(1, 2), (6, 2), (5, 3)$ and $(3, 4)$ , is

Moderate

A

$\frac{3}{2} sq. units$
B

$\frac{11}{2} sq. units$
C

$\frac{1}{2} sq. units$
D

none of these

Solution

We have,
$Δ_{1} = \frac{1}{2} |\begin{array}{ll} 1 6 \\ 2 2 \end{array}| = - 5, Δ_{2} = \frac{1}{2} |\begin{array}{ll} 6 5 \\ 2 3 \end{array}| = 4$
$Δ_{3} = \frac{1}{2} |\begin{array}{ll} 5 3 \\ 3 4 \end{array}| = \frac{11}{2}$ and, $Δ_{4} = \frac{1}{2} |\begin{array}{ll} 3 1 \\ 4 2 \end{array}| = 1$
Area of quadrilateral $= |- 5 + 4 + \frac{11}{2} + 1| = \frac{11}{2}$ sq. units

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