Answer:
[tex]P(x,y) = (\frac{7}{2},2)[/tex]
Step-by-step explanation:
Given
Parallelogram LMNO
[tex]L = (1,4)[/tex]
[tex]M = (7,4)[/tex]
[tex]N = (6,0)[/tex]
[tex]O = (0,0)[/tex]
Required
Determine the point of intersection
The point of intersection of the diagonal is the midpoint of the parallelogram.
The diagonals are: LN and MO
Calculating midpoint, P of LN
[tex]P(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]
Where
[tex]L = (1,4)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]N = (6,0)[/tex] --- [tex](x_2,y_2)[/tex]
So:
[tex]P(x,y) = (\frac{1 + 6}{2},\frac{0 + 4}{2})[/tex]
[tex]P(x,y) = (\frac{7}{2},\frac{4}{2})[/tex]
[tex]P(x,y) = (\frac{7}{2},2)[/tex]
To confirm, we make use of diagonals MO
[tex]M = (7,4)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]O = (0,0)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]P(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]
[tex]P(x,y) = (\frac{7 + 0}{2} , \frac{4 + 0}{2})[/tex]
[tex]P(x,y) = (\frac{7}{2} , \frac{4}{2})[/tex]
[tex]P(x,y) = (\frac{7}{2},2)[/tex]
Hence, the coordinates of the intersection, P is [tex](\frac{7}{2},2)[/tex]
