Question

A = ( 0, - 1 ), B = ( 6, 7 ), C = ( - 2, 3 ) and D = ( 8, 3 ) are four vertices of a quadrilateral ABCD write the type of quadrilateral.​

Answer 1

Answer:

The quadrilateral ABCD can be divided into triangles ABC and ACD and hence the area of the quadrilateral is the sum of the areas of the two triangles.

Area of a triangle with vertices (x

1

,y

1

) ; (x

2

,y

2

) and (x

3

,y

3

) is

∣

∣

∣

∣

∣

2

x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)

∣

∣

∣

∣

∣

Area of quadrilateral ABCD = area of triangle ABC + area of triangle ACD

area of △ABC=

2

1

[−3(−7+8)+(−2)(−8−5)+1(5+7)]

=

2

1

[35] sq. units

area of △ACD=

2

1

[−3(−8−3)+1(3−5)+6(5+8)]

=

2

1

[109] sq. units

Area of quadrilateral ABCD = area of triangle ABC + area of triangle ACD

=

2

1

[35]+

2

1

[109]

=

2

144

=72 sq.units

solution