Question

reasoning a drone flying over a field of corn identifies a dry area. the coordinates of the vertices of the area are shown. to what coordinates should the portable irrigation system be sent to water the dry area? explain your reasoning.

Explanation:

Step1: Recall centroid formula for polygon

For a polygon with vertices $(x_1,y_1),(x_2,y_2),\cdots,(x_n,y_n)$, the centroid $(\bar{x},\bar{y})$ has coordinates $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$ and $\bar{y}=\frac{\sum_{i=1}^{n}y_i}{n}$. Here $n = 4$, $(x_1,y_1)=(56,1012)$, $(x_2,y_2)=(888,1055)$, $(x_3,y_3)=(895,332)$ and $(x_4,y_4)=(144,289)$.

Step2: Calculate x - coordinate of centroid

$\bar{x}=\frac{56 + 888+895 + 144}{4}=\frac{1983}{4}=495.75$.

Step3: Calculate y - coordinate of centroid

$\bar{y}=\frac{1012+1055 + 332+289}{4}=\frac{2688}{4}=672$.

Answer:

$(495.75,672)$