Question

Let E be the point of intersection of the diagonals of a parallelogram. The lengths of the line segments from E to two of the parallelogram’s vertices are 3 meters and 4 meters. What are the lengths of the segments from E to the other two vertices of the parallelogram? Justify your answer.

Answer 1

The length is going to be 3m and 4m.

Answer 2

The diagonals of a parallelogram has the following property:

They bisect each other. Which means each diagonal divides the other diagonal in two equal halves.

So, the point of intersection of two diagonals is the midpoint of both diagonals. If the distance from that point of intersection E, to the vertices of parallelogram is 3 meters and 4 meters, the distance from E to opposite vertices will also be the same i.e. 3 meters and 4 meters respectively, because the diagonals bisect each other.