Question

4. Find the area of the quadrilateral whose vertices are (1,2), (-2,6),(-3,-5) and( 2,-7)
5 Sind by determinants​

Answer 1

Answer:

Answer

(I) Let there be two triangles △ABD and △BCD.

Thus, Area(ABCD)=Area(ABD)+Area(BCD)

Using determinant form to find area, we get

Area(ABCD)=

2

1

∣

∣

∣

∣

∣

∣

∣

∣

1

2

1

1

2

3

1

−1

0

∣

∣

∣

∣

∣

∣

∣

∣

+

2

1

∣

∣

∣

∣

∣

∣

∣

∣

1

2

3

1

−2

2

1

−1

0

∣

∣

∣

∣

∣

∣

∣

∣

Area(ABCD)=12

(II) Let there be two triangles △ABC and △ACD.

Thus, Area(ABCD)=Area(ABC)+Area(ACD)

Using determinant form to find area, we get

Area(ABCD)=

2

1

∣

∣

∣

∣

∣

∣

∣

∣

1

−3

1

1

−2

−2

1

4

1

∣

∣

∣

∣

∣

∣

∣

∣

+

2

1

∣

∣

∣

∣

∣

∣

∣

∣

1

−3

1

1

4

1

1

2

3

∣

∣

∣

∣

∣

∣

∣

∣

Area(ABCD)=17.5 or

2

35

PLs follow and mark

Answer 2

. (9) Find the area of the quadrilateral whose vertices are (1, 2) (- 2, 6) (- 3, - 5) and (2, - 7)