Midpoint formula
We are given the points
X=(-4,2)
Y=(1,-1)
Z=(-2,-3)
W=(1,-4)
They define the quadrilateral XYWZ
To find the intersection of the diagonals, we can use the Midpoint Formula
This formula gives us the midpoint of a segment defined by points (x1,y1) (x2,y2) as follows:
[tex]xm=\frac{x1+x2}{2},\text{ ym=}\frac{y1+y2}{2}[/tex]
We must identify the opposite points of the quadrilateral and calculate the midpoint between them
Segment XY:
Midpoint of XY:
[tex]x_m=\frac{-4+1}{2}=-\frac{3}{2}[/tex][tex]y_m=\frac{2-1}{2}=\frac{1}{2}[/tex]
Midpoint of ZW:
[tex]x_m=\frac{1-2}{2}=-\frac{1}{2}[/tex][tex]y_m=\frac{-3-4}{2}=-\frac{7}{2}[/tex]
Finally, find the midpoint of the opposite sides' midpoints:
[tex]x_c=\frac{-\frac{3}{2}-\frac{1}{2}}{2}=-1[/tex][tex]y_c=\frac{\frac{1}{2}-\frac{7}{2}}{2}=-\frac{3}{2}[/tex]
The intersection of the diagonals is the point (-1,-3/2)
