Question

A fish and wildlife management organization uses a GIS (Geographic Information System) to store and analyze data for the parcels of land it manages. All of the parcels are mapped on a grid in which 1 unit represents 1 acre. If the coordinates of the corners of a parcel are (-8, 10), (6, 17) and (2, -4), how many acres is the parcel? a. 150 acres c. 133 acres b. 125 acres d. 167 acres

Answer 1

c. 133 acres

Explanation:

Given: coordinates of the corners of a parcel are (-8, 10), (6, 17) and (2, -4)

To find: area of the parcel

Solution:

Using heron's formula,

area of triangle joining coordinates
`(x_1,y_1),(x_2,y_2),(x_3,y_3)` is equal to
`(1)/(2)|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|`

Let
`(x_1,y_1)=(-8,10)\,,\,(x_2,y_2)=(6,17)\,,\,(x_3,y_3)=(2,-4)`

Area of triangle (parcel)
`=(1)/(2)|-8(17+4)+6(-4-10)+2(10-17)|\\`
`=(1)/(2)|-8(21)+6(-14)+2(-7)|\\ =(1)/(2)|-168-84-14|\\ =(1)/(2)|-266|\\ =133\,\,acres`