Quadrilateral ABCD – parallelogram, B (-2; 3), C (10; 9), D (7; 0). Know the coordinates of the vertex A

Let the point O with coordinates (X; Y) be the point of intersection of the diagonals of the parallelogram, and therefore is the midpoint of the diagonal BD.

Then, X = (-2 + 7) / 2 = 2.5.

Y = (3 + 0) / 2 = 1.5.

Point O is also the middle of the AC diagonal. Let the coordinates of point A be (X1; Y1), then:

(X1 + 10) / 2 = 2.5.

X1 = 2.5 * 2 – 10 = -5.

(Y1 + 9) / 2 = 1.5.

Y1 = 3 – 9 = -6.

Point A has coordinates (-5; -6).

Answer: The coordinates of the vertex are equal to A (-5; -6)