if A(-2,3) B(6,5 ) C (x,-5) D(-4,-3) are the vertices of a quadrilateral ABCD of area 80sq unit then find - Maths -

Question

if A(-2,3) B(6,5 ) C (x,-5) D(-4,-3) are the vertices of a
quadrilateral ABCD of area 80sq unit then find positive value of
x

Somnath maths · Accepted Answer

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Given,
x1=−2,x2=6,x3=x,x4=−4y1=3,y2=5,y3=−5,y4=−3Given,
Area of quadrilateral=80 sq cmArea of quadrilateral=Area of
ΔABC+Area of ΔADCNow, for
ΔABC,x1=−2,x2=6,x3=xy1=3,y2=5,y3=−5 ∴Area
of
ΔABC=12|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|=12|−2(5+5)+6(−5−3)+x(3−5)|=12|−2x−68|=x+34Area
of
ΔACD=12|−2(−5+3)+x(−3−3)+(−4)(3+5)|=12|−6x−12|=3x+6
∴area of quad ABCD=x+34+3x+6=>80=4x+40=>4x=40=>x=10

if A(-2,3) B(6,5 ) C (x,-5) D(-4,-3) are the vertices of a quadrilateral ABCD of area 80sq unit then find positive value of x