Show that points (1,1),(4,4),(4,8)and (1,5) are the vertices of a parallelogram.
Answers
Answer:
Let the points (4, 5) (7, 6) (4, 3) (1, 2) represent the points A, B, C and D.
AB = √[(7 - 4)2 + (6 - 5)2] = √(9 + 1) = √10
BC = √[(4 - 7)2 + (3 - 6)2] = √(9 + 9) = √18
CD = √[(1 - 4)2 + (2 - 3)2] = √(9 + 1) = √10
DA = √[(1 - 4)2 + (2 - 5)2] = √(9 + 9) = √18
AC = √[(4 - 4)2 + (3 - 5)2] = √(0 + 4) = √4 = 2
BD = √[(1 - 7)2 + (2 - 6)2] = √(36 + 16) = √52 = 2√13
Opposite sides of the quadrilateral formed by the given four points are equal.
Also the diagonals are unequal.
Therefore, the given points form a parallelogram.
hope helpfull to you
Answer :
Refer to the attachment.
More about parallelogram :
★ Opposite sides are equal.
★ Opposite sides are parallel.
★ Diagonals bisect each other.
★ Diagonal divide the parallelogram in two congruent triangles.
★ Area of triangle is half the area of parallelogram.
★ Area of parallelogram = Base × Height