Question

Find the coordinates of the intersection of the diagonals of parallelogram $GHJK$ with vertices $G\left(1,3\right),\ H\left(4,3\right),\ J\left(5,1\right),$ and $K\left(2,1\right).$

Answer 1

Concept:

A simple (non-self-intersecting) quadrilateral with two sets of parallel sides is called a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

If a quadrilateral is a parallelogram, then the diagonals bisect each other

Given:

G(1,3):H(4,3):J(4,3): K(2,1)

Find:

Find the coordinates of the intersection of the diagonals of parallelogram GHJK

Solution:

If a quadrilateral is a parallelogram, then the diagonals bisect each other

So, midpoint of GJ=((1+5)/2,(3+1)/2)

                               =(3,2)

Similarly, Midpoint of HK=((4+2)/2,(3+1)/2)

                                         =(3,2)

Therefore, the coordinates of the intersection of the diagonals pf paralLelogram =(3,2)

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