Question

show that(1,1) (4,4) (4,8) (1,5) are the vertices of a parallelogram

Answer 1

Step-by-step explanation:

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.

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