Respuesta :
Answer:
c. 133 acres
Step-by-step 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 [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] is equal to [tex]\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Let [tex](x_1,y_1)=(-8,10)\,,\,(x_2,y_2)=(6,17)\,,\,(x_3,y_3)=(2,-4)[/tex]
Area of triangle (parcel) [tex]=\frac{1}{2}|-8(17+4)+6(-4-10)+2(10-17)|\\[/tex] [tex]=\frac{1}{2}|-8(21)+6(-14)+2(-7)|\\ =\frac{1}{2}|-168-84-14|\\ =\frac{1}{2}|-266|\\ =133\,\,acres[/tex]
