# Point O (0; 0) point A (11; -4) point B (11; 12), C (0; 16), are the vertices of the quadrilateral

Point O (0; 0) point A (11; -4) point B (11; 12), C (0; 16), are the vertices of the quadrilateral, find the abscissa of the point P of the intersection of its diagonals.

Point O (0; 0) point A (11; – 4) point B (11; 12), C (0; 16), are the vertices of the quadrilateral, we need to find the abscissa of the point P of intersection of its diagonals. First, we find the sides of the quadrangle:

BA (11 – 11; 12 + 4) = BA (0; 16);

CB (11 – 0; 12 – 16) = CB (11; – 4);

OS (0; 16);

OA (11; – 4).

The opposite sides are pairwise equal, the quadrilateral is a parallelogram, which means that point P is the midpoint of the OB segment. Let’s find the middle of the segment OB:

x = (11 + 0) / 2 = 5.5 and y = (12 + 0) / 2 = 6.

Answer: the abscissa of point P is 5.5.

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