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( (x_1+x_2)/(2), (y_1+y_2)/(2)\right )`

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

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

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

Using this midpoint find the missing coordinate.

`$\text{Midpoint} =\left( (x_1+x_2)/(2), (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( (0+x)/(2), (0+y)/(2)\right )`

`$\left( (m+h)/(2), (n)/(2)\right )=\left( (0+x)/(2), (0+y)/(2)\right )`

`$\left( (m+h)/(2), (n)/(2)\right )=\left( (x)/(2), (y)/(2)\right )`

Now equate the x-coordinates and y-coordinates.

`$ (m+h)/(2)=(x)/(2), \ \ \ (n)/(2) = (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).