Question

Find the coordinates of the intersection of the diagnosis of the parallelograms (-2,-1) (1,3) (6,3) and (3,-1)

Answer 1

`M = (2,1)`

Explanation:

Represent the diagonals as:

`A =(-2,-1)`

`B =(1,3)`

`C =(6,3)`

`D = (3,-1)`

Required

Determine the coordinate of the intersection

To do this, we simply calculate the midpoint of AC or BD.

For AC:

`(x_1,y_1) = (-2,-1)`

`(x_2,y_2) = (6,3)`

The midpoint is:

`M = (1)/(2)\{(x_1+x_2),(y_1+y_2)\}`

This gives:

`M = (1)/(2)\{(-2+6),(-1+3)\}`

`M = (1)/(2)\{(4),(2)\}`

`M = ((1)/(2) * 4,(1)/(2) * 2)`

`M = (2,1)`

For BD:

`(x_1,y_1) = (1,3)`

`(x_2,y_2) = (3,-1)`

The midpoint is:

`M = (1)/(2)\{(x_1+x_2),(y_1+y_2)\}`

This gives:

`M = (1)/(2)\{(1+3),(3-1)\}`

`M = (1)/(2)\{(4),(2)\}`

`M = ((1)/(2) * 4,(1)/(2) * 2)`

`M = (2,1)`

Notice the midpoints are the same:

`M = (2,1)`

Hence, the coordinates of the intersection is (2,1)