Answer:
[tex]M = (2,1)[/tex]
Step-by-step explanation:
Represent the diagonals as:
[tex]A =(-2,-1)[/tex]
[tex]B =(1,3)[/tex]
[tex]C =(6,3)[/tex]
[tex]D = (3,-1)[/tex]
Required
Determine the coordinate of the intersection
To do this, we simply calculate the midpoint of AC or BD.
For AC:
[tex](x_1,y_1) = (-2,-1)[/tex]
[tex](x_2,y_2) = (6,3)[/tex]
The midpoint is:
[tex]M = \frac{1}{2}\{(x_1+x_2),(y_1+y_2)\}[/tex]
This gives:
[tex]M = \frac{1}{2}\{(-2+6),(-1+3)\}[/tex]
[tex]M = \frac{1}{2}\{(4),(2)\}[/tex]
[tex]M = (\frac{1}{2} * 4,\frac{1}{2} * 2)[/tex]
[tex]M = (2,1)[/tex]
For BD:
[tex](x_1,y_1) = (1,3)[/tex]
[tex](x_2,y_2) = (3,-1)[/tex]
The midpoint is:
[tex]M = \frac{1}{2}\{(x_1+x_2),(y_1+y_2)\}[/tex]
This gives:
[tex]M = \frac{1}{2}\{(1+3),(3-1)\}[/tex]
[tex]M = \frac{1}{2}\{(4),(2)\}[/tex]
[tex]M = (\frac{1}{2} * 4,\frac{1}{2} * 2)[/tex]
[tex]M = (2,1)[/tex]
Notice the midpoints are the same:
[tex]M = (2,1)[/tex]
Hence, the coordinates of the intersection is (2,1)
