Answer:
Step-by-step explanation:
To find the area of a triangle given its three vertices, you can use the Shoelace Formula (also known as Gauss's area formula or the surveyor's formula). The formula involves computing the sum of the products of the coordinates of consecutive vertices, and then subtracting the sum of the products of the coordinates of consecutive vertices in reverse order. Here's how you can apply the formula to find the area of the triangle with the given vertices (8,1), (10,0), and (6,0):
Write down the coordinates of the vertices in a counterclockwise order: (8,1), (10,0), (6,0), (8,1).
Multiply the coordinates of each vertex pair and write down the results: (8 × 0) + (10 × 0) + (6 × 1) = 6.
Multiply the coordinates of each pair in reverse order and write down the results: (1 × 10) + (0 × 6) + (0 × 8) = 10.
Calculate the absolute value of the difference between the two sums: |6 - 10| = 4.
Divide the result by 2 to obtain the area of the triangle: 4 / 2 = 2 square units.
Therefore, the area of the triangle with the vertices (8,1), (10,0), and (6,0) is 2 square units.
