Question

What are the missing coordinates? My teacher said it was (h-m,n), but I’m saying it is (h+m,n). Could anyone help? (16 points)

Answer 1

The missing coordinates of the parallelogram is (m + h, n).

Solution:

Property of parallelogram,

Diagonals of the parallelogram bisect each other.

Solve using mid-point formula:

$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right )$

Here $x_1=m, y_1=n, x_2=h, y_2=0$

              $=\left( \frac{m+h}{2}, \frac{n+0}{2}\right )$

$\text{Midpoint} =\left( \frac{m+h}{2}, \frac{n}{2}\right )$

To find the missing coordinate:

Let the missing coordinates by x and y.

Here $x_1=0, y_1=0, x_2=x, y_2=y$

$\text{Midpoint}=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )$

$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{x}{2}, \frac{y}{2}\right )$

Now equate the x-coordinate.

$\frac{m+h}{2}=\frac{x}{2}$

Multiply by 2 on both sides of the equation, we get

x = m + h

Now equate the y-coordinate.

$\frac{n}{2} = \frac{y}{2}$

Multiply by 2 on both sides of the equation, we get

y = n

The coordinates are (m+h, n).

Hence the missing coordinates of the parallelogram is (m + h, n).