Show that the points A (1,- 2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Answers
Here to prove that above mentioned points are the vertices of a parallelogram, we have to focus on the properties of a parallelogram.
Explanation:
So what we have here:-
A = (1,-2)
B = (3, 6)
C = (5, 10)
D = (3, 2)
AB and CD are opposite sides.
So if opposite sides are equal then it is a parallelogram.
A = (1, -2)
B = (3, 6)
Length of AB =length along the x-axis = 3 – 1 = 2.
C = (5, 10)
D = (3, 2)
Length of CD = length along x –axis = 5 – 3 = 2.
As AB = CD so they are of equal length.
Now for AD and BC
Length of BC = length along y axis = 10 – 6 = 4.
Length of AD = length along y-axis = 2 – (-2) = 2 + 2 = 4.
As BC = AD so opposite sides are equal length.
As opposite sides are of equal length so the points are the vertices of a parallelogram.
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