Given three vertices of the parallelogram ABCD- A (-1; 1), B (0; 3), C (5; 7). Find the coordinates of the intersection

Given three vertices of the parallelogram ABCD- A (-1; 1), B (0; 3), C (5; 7). Find the coordinates of the intersection of the diagonals and the coordinates of the fourth vertex.

The coordinates of the midpoint of the segment AC (point O) will be the coordinates of the intersection of the diagonals:

XO = (XA + XC) / 2 = (-1 + 5) / 2 = 2;

YO = (YA + YC) / 2 = (1 + 7) / 2 = 4;

The point O (2; 4) will also be the midpoint of the diagonal BD. We denote the coordinates of point D as XD and YD and write through them the coordinates of point O:

XO = (XB + XD) / 2;

2 = (0 + XD) / 2;

XD = 4;

YO = (YB + YD) / 2;

4 = (3 + YD) / 2;

8 = 3 + YD;

YD = 5.

Answer. The intersection point is O (2; 4), the fourth vertex is D (4; 5).