Question

Parallelogram LMNO has the coordinates L(1, 4), M(7, 4), N(6, 0) and O(0, 0). The diagonals of Parallelogram LMNO intersect at point P. What are the coordinates of point P?

Answer 1

L(1, 4), M(7, 4), N(6, 0)

Explanation:

Answer 2

`P(x,y) = ((7)/(2),2)`

Explanation:

Given

Parallelogram LMNO

`L = (1,4)`

`M = (7,4)`

`N = (6,0)`

`O = (0,0)`

Required

Determine the point of intersection

The point of intersection of the diagonal is the midpoint of the parallelogram.

The diagonals are: LN and MO

Calculating midpoint, P of LN

`P(x,y) = ((x_1 + x_2)/(2),(y_1 + y_2)/(2))`

Where

`L = (1,4)` ---
`(x_1,y_1)`

`N = (6,0)` ---
`(x_2,y_2)`

So:

`P(x,y) = ((1 + 6)/(2),(0 + 4)/(2))`

`P(x,y) = ((7)/(2),(4)/(2))`

`P(x,y) = ((7)/(2),2)`

To confirm, we make use of diagonals MO

`M = (7,4)` ---
`(x_1,y_1)`

`O = (0,0)` ---
`(x_2,y_2)`

`P(x,y) = ((x_1 + x_2)/(2),(y_1 + y_2)/(2))`

`P(x,y) = ((7 + 0)/(2) , (4 + 0)/(2))`

`P(x,y) = ((7)/(2) , (4)/(2))`

`P(x,y) = ((7)/(2),2)`

Hence, the coordinates of the intersection, P is
`((7)/(2),2)`