Answer:
The coordinates of the intersection of the diagonal of the parallelogram are [tex]M(x,y) = (3,2)[/tex].
Step-by-step explanation:
Diagonals are represented by line segments GJ and KH. Since quadrilateral is a parallelogram, then coordinates of the intersection are located at midpoint of each diagonal ([tex]M(x,y)[/tex]). That is:
[tex]M(x,y) = G(x,y) + \frac{1}{2}\cdot \overrightarrow {GJ}[/tex]
[tex]M(x,y) = G(x,y) +\frac{1}{2}\cdot [J(x,y)-G(x,y)][/tex] (1)
If we know that [tex]G(x,y) = (1,3)[/tex] and [tex]J(x,y) = (5,1)[/tex], the coordinates of the intersection of the diagonals of the parallelogram are:
[tex]M(x,y) = (1,3) +\frac{1}{2}\cdot [(5,1)-(1,3)][/tex]
[tex]M(x,y) = (1,3) +\frac{1}{2}\cdot (4,-2)[/tex]
[tex]M(x,y) = (1,3) +(2,-1)[/tex]
[tex]M(x,y) = (3,2)[/tex]
There is another form:
[tex]M(x,y) = K(x,y) +\frac{1}{2}\cdot \overrightarrow{KH}[/tex]
[tex]M(x,y) = K(x,y) + \frac{1}{2}\cdot [H(x,y)-K(x,y)][/tex] (2)
If we know that [tex]K(x,y) = (2, 1)[/tex] and [tex]H(x,y) = (4,3)[/tex], the coordinates of the intersection of the diagonals of the parallelogram are:
[tex]M(x,y) = (2,1) + \frac{1}{2}\cdot [(4,3)-(2,1)][/tex]
[tex]M(x,y) = (2,1) + \frac{1}{2} \cdot (2,2)[/tex]
[tex]M(x,y) = (2,1) + (1,1)[/tex]
[tex]M(x,y) = (3,2)[/tex]
Therefore, the coordinates of the intersection of the diagonal of the parallelogram are [tex]M(x,y) = (3,2)[/tex].
