Question

using determinant method find the area of the quadrilateral ABCD given the coordinates A(3,3) B(-2,5) c(-1,2) D(1,1)

Answer 1

Make sure the points given are listed as consecutive points of the figure, either clockwise or counterclockwise. They are.

list them in a column, starting with any point, I will start with A
3 3
-2 5
-1 2
1 1
3 3 , you repeat the first one you started with

Area = | (1/2)(downproducts - upproducts) |
= (1/2)(15 - 4 - 1 + 3 -(-6 -5 + 2 + 3))
= (1/2)( 13 + 6)
= 19/2 or 9.5 square units

Answer 2

±1/2[3(4) -3(-3) +1(-7) -2(-1) -5(2) +1(3)]
±1/2[12+9-7+2-10]
±1/2[21-7+2-10]
±1/2[14+2-10]
±1/2[16-10]
1/2×6
6/2
So, answer is 3