Answer:
Length = 50 units
width = 35 units
Step-by-step explanation:
Let A, B, C and D be the corner of the pools.
Given:
The points of the corners are.
![A(x_{1}, y_{1}})=(-20, 25)](https://tex.z-dn.net/?f=A%28x_%7B1%7D%2C%20y_%7B1%7D%7D%29%3D%28-20%2C%2025%29)
![B(x_{2}, y_{2}})=(30, 25)](https://tex.z-dn.net/?f=B%28x_%7B2%7D%2C%20y_%7B2%7D%7D%29%3D%2830%2C%2025%29)
![C(x_{3}, y_{3}})=(30, -10)](https://tex.z-dn.net/?f=C%28x_%7B3%7D%2C%20y_%7B3%7D%7D%29%3D%2830%2C%20-10%29)
![D(x_{4}, y_{4}})=(-20, -10)](https://tex.z-dn.net/?f=D%28x_%7B4%7D%2C%20y_%7B4%7D%7D%29%3D%28-20%2C%20-10%29)
We need to find the dimension of the pools.
Solution:
Using distance formula of the two points.
----------(1)
For point AB
Substitute points A(30, 25) and B(30, 25) in above equation.
![AB=\sqrt{(30-(-20))^{2}+(25-25)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%2830-%28-20%29%29%5E%7B2%7D%2B%2825-25%29%5E%7B2%7D%7D)
![AB=\sqrt{(30+20)^{2}}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%2830%2B20%29%5E%7B2%7D%7D)
![AB=\sqrt{(50)^{2}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%2850%29%5E%7B2%7D)
AB = 50 units
Similarly for point BC
Substitute points B(-20, 25) and C(30, -10) in equation 1.
![d(B,C)=\sqrt{(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}](https://tex.z-dn.net/?f=d%28B%2CC%29%3D%5Csqrt%7B%28x_%7B3%7D-x_%7B2%7D%29%5E%7B2%7D%2B%28y_%7B3%7D-y_%7B2%7D%29%5E%7B2%7D%7D)
![BC=\sqrt{(30-30)^{2}+((-10)-25)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%2830-30%29%5E%7B2%7D%2B%28%28-10%29-25%29%5E%7B2%7D%7D)
![BC=\sqrt{(-35)^{2}}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%28-35%29%5E%7B2%7D%7D)
BC = 35 units
Similarly for point DC
Substitute points D(-20, -10) and C(30, -10) in equation 1.
![d(D,C)=\sqrt{(x_{3}-x_{4})^{2}+(y_{3}-y_{4})^{2}}](https://tex.z-dn.net/?f=d%28D%2CC%29%3D%5Csqrt%7B%28x_%7B3%7D-x_%7B4%7D%29%5E%7B2%7D%2B%28y_%7B3%7D-y_%7B4%7D%29%5E%7B2%7D%7D)
![DC=\sqrt{(30-(-20))^{2}+(-10-(-10))^{2}}](https://tex.z-dn.net/?f=DC%3D%5Csqrt%7B%2830-%28-20%29%29%5E%7B2%7D%2B%28-10-%28-10%29%29%5E%7B2%7D%7D)
![DC=\sqrt{(30+20)^{2}}](https://tex.z-dn.net/?f=DC%3D%5Csqrt%7B%2830%2B20%29%5E%7B2%7D%7D)
![DC=\sqrt{(50)^{2}}](https://tex.z-dn.net/?f=DC%3D%5Csqrt%7B%2850%29%5E%7B2%7D%7D)
DC = 50 units
Similarly for segment AD
Substitute points A(-20, 25) and D(-20, -10) in equation 1.
![d(A,D)=\sqrt{(x_{4}-x_{1})^{2}+(y_{4}-y_{1})^{2}}](https://tex.z-dn.net/?f=d%28A%2CD%29%3D%5Csqrt%7B%28x_%7B4%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B4%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
![AD=\sqrt{(-20-(-20))^{2}+(-10-25)^{2}}](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%28-20-%28-20%29%29%5E%7B2%7D%2B%28-10-25%29%5E%7B2%7D%7D)
![AD=\sqrt{(-20+20)^{2}+(-35)^{2}}](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%28-20%2B20%29%5E%7B2%7D%2B%28-35%29%5E%7B2%7D%7D)
![AD=\sqrt{(-35)^{2}}](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%28-35%29%5E%7B2%7D%7D)
AD = 35 units
Therefore, the dimension of the rectangular swimming pool are.
Length = 50 units
width = 35 units