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
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The equation of first diagonal is
[tex]y-(-2)=\frac{-7-(-2)}{4-(-3)}(x-(-3))[/tex]
[tex]y+2=\frac{-5}{7}(x+3)[/tex]
[tex]7y+14=-5(x+3)[/tex]
[tex]7y+14=-5x-15[/tex]
[tex]5x+7y=-29[/tex] .... (1)
The equation of second diagonal is
[tex]y-(-2)=\frac{-7-(-2)}{-3-4}(x-4)[/tex]
[tex]y+2=\frac{-5}{-7}(x-4)[/tex]
[tex]7y+14=5(x-4)[/tex]
[tex]7y+14=5x-20[/tex]
[tex]5x-7y=34[/tex] .... (2)
Add equation (1) and (2),
[tex]10x=5[/tex]
[tex]x=0.5[/tex]
Put this value in (1).
[tex]5(0.5)+7y=-29[/tex]
[tex]y=-4.5[/tex]
The intersection point of diagonals is (0.5,-4.5).
