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# Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

Q : 1     Draw a quadrilateral in the Cartesian plane, whose vertices are $(-4,5),(0,7),(5,-5)$  and  $(-4,-2)$. Also, find its area.

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Area of ABCD = Area of ABC + Area of ACD
Now, we know that the area of a triangle with vertices $(x_1,y_1),(x_2,y_2) \ and \ (x_3,y_3)$  is given by
$A = \frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$
Therefore,
Area of triangle ABC $= \frac{1}{2}|-4(7+5)+0(-5-5)+5(5-7)|= \frac{1}{2}|-48-10|= \frac{58}{2}=29$
Similarly,
Area of triangle ACD $= \frac{1}{2}|-4(-5+2)+5(-2-5)+-4(5+5)|= \frac{1}{2}|12-35-40|= \frac{63}{2}$
Now,
Area of ABCD = Area of ABC + Area of ACD
$=29+\frac{63}{2}$
$=\frac{121}{2} \ units$

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