Given a quadrilateral whose vertices are ( 3, 5 ) , ( 4, -1 ), ( 8, -2 ) and ( 9, 7 ), show that the line segments joining the midpoints of adjacent sides from a parallelogram.

Question

A lesson about Division of a Line Segment and Midpoint of a Line Segment

Answer 1

( 3, 5 ) , ( 4, -1 ), ( 8, -2 ) and ( 9, 7 )

midpoint1 = (3.5,2)

midpoint2= (6,-1.5)

midpoint3= (8.5,2.5)

midpoint4= (6,6)

slope 1 to 2 =-3.5/2.5

slope 4 to 3 = -3.5/2.5

two opposite sides parallel

slope 2 to 3 =4/2.5

slope 1 to 4 =4/2.5

other two sides opposite parallel

quadrilateral with opposite sides parallel is a parallelogram.

Answer 2

This is true for any convex quadraliteral, because if we combine midpoints of adgaisent sides we get parallelogram (opposite sides parallel and equal half of diagonals) and diagonals of parallelogram bysect each other