Question

Can anyone help me find the (?,?) coordinates? The given shape is a parallelogram.

Answer 1

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:

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

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

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

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

Using this midpoint find the missing coordinate.

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

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-coordinates and y-coordinates.

$\frac{m+h}{2}=\frac{x}{2}, \ \ \ \frac{n}{2} = \frac{y}{2}$

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).