# Points A (0; -2), B (3; -4), D (1; -1) are the vertices of the ABCD parallelogram. find the coordinates of the vertex C.

Suppose that the point O (x; y) is the intersection point of the diagonals AC and BD. As you know, in a parallelogram, the diagonals intersect and are halved at the intersection point. Therefore, point O is the midpoint of the segment BD, we find its coordinates

x = (3 + 1) / 2 = 4/2 = 2;

y = (-4 + (-1)) / 2 = -5 / 2 = -2.5.

Point O has coordinates (2; -2.5).

Let us denote the coordinates of the point C through (x; y).

Point O is the middle of the segment AC, therefore, having compiled and solved the equations, we will find the coordinates of point C:

(0 + x) / 2 = 2;

x / 2 = 2;

x = 2 * 2;

x = 4.

(-2 + y) / 2 = -2.5;

-2 + y = -2.5 * 2;

-2 + y = -5;

y = -5 – (-2);

y = -5 + 2;

y = -3.

The coordinates of the vertex C are equal to (4; -3).

Answer: vertex C has coordinates (4; -3).