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

Question

asked Mar 14, 2022 80.8k views

1 Answer

Rick Liao · Answer 1 · 2022-03-20T23:51:20+0000

Answer:

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)