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).

Step-by-step 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) = ($\frac{(x1+x2)}{2}$ , $\frac{(y1+y2)}{2}$)

         = ($\frac{(-1+5)}{2}$ , $\frac{(10+4)}{2}$)

      = ($\frac{4}{2}$, $\frac{14}{2}$)

     = (2,7)

       

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