Jonas is planning to use part of the land behind his house to have a soccer field. Jonas plots his soccer field plan on a grid. A side of each square on the grid is equal to two meters. Two of the vertices of the soccer field are at (4, 8) and (10, 4). If the soccer field is a rectangle, what are the coordinates of the other two vertices? Jonas is planning to build a fence around the soccer field. How many meters of fencing does Jonas need to put around the soccer field? How much of the land behind his house is located inside the fence? Show all your mathematical thinking. 4,8 10,8 4,4 10,4

The other two vertices have coordinates (4,4) and (10,8). He will need 40 meters of fence for the soccer field. And inside the fence there are 48 square meters, which is a 24% of the total surface of the land behind his house, assuming it is a square of 10 meters of lengt and 10 meters of width.

Step-by-step explanation:

Since the coordinates must form a rectange, then, the other two location must be (4,4) and (10,8) (each coordinate must have something in common with the coordinates of the 2 locations we were given).

The sides of the fence have length 8-4 = 4, and 10-4 = 6. Thus, the perimeter of the fence is 2*4+2*6 = 20 units. Since each unit is 2 meters, then that means that Jonas will need 40 meters of fence.

The area inside the fence is 6*4 = 24 square units, therefore it is 48 square meters, and assuming that the grid goes from 0 to 10 in both coordinates, the area of the land behind his house is 10*10 = 100 square units, thus it is 200 square meters. He is using 48/200*100 = 24% of the land for the soccer field.