The missing coordinates of the parallelogram is (m + h, n).
Solution:
Given shape is a parallelogram.
Construction: Draw a line joining the diagonals.
In parallelogram, diagonals bisect each other.
Solve it using mid-point formula:
[tex]$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right )[/tex]
Here [tex]x_1=m, y_1=n, x_2=h, y_2=0[/tex]
[tex]$\text{Midpoint} =\left( \frac{m+h}{2}, \frac{n+0}{2}\right )[/tex]
[tex]$\text{Midpoint} =\left( \frac{m+h}{2}, \frac{n}{2}\right )[/tex]
Using this midpoint find the missing coordinate.
[tex]$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right )[/tex]
Let the missing coordinates by x and y.
Here [tex]x_1=0, y_1=0, x_2=x, y_2=y[/tex]
[tex]$\text{Midpoint}=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )[/tex]
[tex]$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )[/tex]
[tex]$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{x}{2}, \frac{y}{2}\right )[/tex]
Now equate the x-coordinates and y-coordinates.
[tex]$ \frac{m+h}{2}=\frac{x}{2}, \ \ \ \frac{n}{2} = \frac{y}{2}[/tex]
Multiply by 2 on both sides of the equation, we get
m + h = x, n = y
x = m + h and y = n
Hence the missing coordinates of the parallelogram is (m + h, n).