Question

Parallelogram ABCD has coordinates A(-1,10) B(2, -1) C(5,4) and D(-4,5). Find the coordinates of where diagonals AC and BD intersect at. Enter your answers as numbers.

Answer 1

The coordinates of where diagonals AC and BD intersect at O(2,7).

Explanation:

We are given coordinates as A(-1,10) and C(5,4).And we know that the diagonals of parallelogram always bisect each other.

Let us consider O is the intersection point among the diagonals AC and BD. So, the point O bisects the line AC into two equal parts, and also it is the mid-point of AC.

We can find point O using the midpoint formula as,

O (x,y) = (
`((x1+x2))/(2)` ,
`((y1+y2))/(2)`)

= (
`((-1+5))/(2)` ,
`((10+4))/(2)`)

= (
`(4)/(2)`,
`(14)/(2)`)

= (2,7)

So Diagonals AC and BD intersects at the point O (2,7).