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).
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