Answer:
The intersection point of diagonals is (0.5,-4.5).
Step-by-step explanation:
The end points of first diagonal are p(-3, -2) and i(4, -7).
The end points of second diagonal are a(4, -2) and d(-3, -7).
If a line passing through two points, then the equation of line is
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
The equation of first diagonal is
![y-(-2)=\frac{-7-(-2)}{4-(-3)}(x-(-3))](https://tex.z-dn.net/?f=y-%28-2%29%3D%5Cfrac%7B-7-%28-2%29%7D%7B4-%28-3%29%7D%28x-%28-3%29%29)
![y+2=\frac{-5}{7}(x+3)](https://tex.z-dn.net/?f=y%2B2%3D%5Cfrac%7B-5%7D%7B7%7D%28x%2B3%29)
![7y+14=-5(x+3)](https://tex.z-dn.net/?f=7y%2B14%3D-5%28x%2B3%29)
![7y+14=-5x-15](https://tex.z-dn.net/?f=7y%2B14%3D-5x-15)
.... (1)
The equation of second diagonal is
![y-(-2)=\frac{-7-(-2)}{-3-4}(x-4)](https://tex.z-dn.net/?f=y-%28-2%29%3D%5Cfrac%7B-7-%28-2%29%7D%7B-3-4%7D%28x-4%29)
![y+2=\frac{-5}{-7}(x-4)](https://tex.z-dn.net/?f=y%2B2%3D%5Cfrac%7B-5%7D%7B-7%7D%28x-4%29)
![7y+14=5(x-4)](https://tex.z-dn.net/?f=7y%2B14%3D5%28x-4%29)
![7y+14=5x-20](https://tex.z-dn.net/?f=7y%2B14%3D5x-20)
.... (2)
Add equation (1) and (2),
![10x=5](https://tex.z-dn.net/?f=10x%3D5)
![x=0.5](https://tex.z-dn.net/?f=x%3D0.5)
Put this value in (1).
![5(0.5)+7y=-29](https://tex.z-dn.net/?f=5%280.5%29%2B7y%3D-29)
![y=-4.5](https://tex.z-dn.net/?f=y%3D-4.5)
The intersection point of diagonals is (0.5,-4.5).