Question

The vertices of a quadrilateral are (3,-2), (-3, 4), (1,8) and (7,4). Prove that the line joining
the mid points of the sides of a quadrilateral in the same order form a parallelogram.​

Answer 1

Answer:

Step-by-step explanation:

The midpoint of vertices (1,8) and (3,4) = (1+3/2, 8+4/2) = (2,6)

The midpoint of vertices (3,4) and (3,-2) = (3+3/2, 4-2/2) = (3,1)

The midpoint of vertices (7,4) and (3,-2) = (7+3/2, 4-2/2) = (5,1)

The midpoint of vertices (7,4) and (1,8)  = (7+1/2, 4+8/2) =  (4,6)

Now find the distance between the midpoints which is the length of the side of the parallelogram.

The distance between points (3,1) and (5,1) = 2.

The distance between points (2,6) and (4,6) = 2.

Thus the line joining (2,6) and (4,6)is parallel to the line joining (3,1) and (5,1)and they have equal length of 2.

This forms a quadrilateral having one pair of opposite sides equal and parallel so the quadrilateral is a parallelogram.

Answer 2

Step-by-step explanation:

here is ur answer..,.....