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)
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
To find the area of a quadrilateral using the determinant method, you can follow these steps:
1. Label the coordinates of the vertices of the quadrilateral. In this case, we have:
A(3,3), B(-2,5), C(-1,2), and D(1,1).
2. Write down the coordinates of the vertices as matrices. The matrix form of the coordinates is:
A = [3, 3]
B = [-2, 5]
C = [-1, 2]
D = [1, 1]
3. Set up the matrix for the determinant method. Create a matrix with the x-coordinates in the first column and the y-coordinates in the second column. Repeat the first coordinate as the last column to complete the matrix. The matrix will be:
[3, 3, 1]
[-2, 5, -2]
[-1, 2, -1]
[1, 1, 3]
4. Calculate the determinants of the matrix. The area of the quadrilateral can be found by taking half of the absolute value of the determinant of the matrix formed:
Area = 1/2 * |determinant|
Using the formula to calculate the determinant:
Area = 1/2 * [(3*5*3) + (-2*2*1) + (-1*1*1) - (1*5*1) - (-1*2*3) - (3*2*1)]
5. Simplify the expression and calculate the area:
Area = 1/2 * [(45) + (-4) + (-1) - (5) - (-6) - (6)]
Area = 1/2 * (35)
Area = 17.5
Therefore, the area of the quadrilateral ABCD is 17.5 square units.
±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