Question

the landscape designer is trying to build a sitting area halfway between the centers of the sitting - set and the garden shed. use the image of the backyard layout. where should the sitting area go? backyard layout

Explanation:

Step1: Find mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Assume the center of the sitting set is $(x_2,y_2)=(10,4)$ and the center of the garden shed is $(x_1,y_1)=(4,9)$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{4 + 10}{2}=\frac{14}{2}=7$.

Step3: Calculate y - coordinate of mid - point

$y=\frac{9+4}{2}=\frac{13}{2}=6.5$.
The mid - point is $(7,6.5)$ but since it's not in the options, if we assume we are just looking at integer - based approximations and a more visual mid - point between the regions, we consider the closest reasonable point. If we assume we want to split the distance in a more intuitive grid - based way between the two general areas, the mid - point between the areas of the sitting set and garden shed in a simple sense would be $(6.5,6.5)$ as it is in the middle of the grid squares between the two regions.

Answer:

$(6.5,6.5)$