How to find the point of intersections of diagonals?

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Answer 1 · 2018-02-12T09:49:11

As detailed below

Since, the shape is not given, let us consider the following cases of a quadrilateral with coordinates of four corners given :

Case 1 : Nonuniform quadrlateral.
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Knowing the coordinates of ABCD, we can find the equation of AC & BD using the standard for of equation,

#(y-y1) / (y2 - y1) = (x-x1) / (x2-x1)#

By solving the two equations we can find the intersection point O.

Case 2 : Square or rectangle or rhombus or parallelogram
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In all these four shapes, diagonals bisect each other.

Using mid point formula, we can find the intersection point.

#(x,y) = ((x1 + x2) /2, (y1 + y2) / 2)#

Case 3 : Trapezoid or Kite
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Similar to a quadrilateral. By solving the equations of the diagonals, one can arrive at the intersection point.