Show that the
points A (0, 0), B(3, 0),
C(4, 1) and D(1, 1)
form a parallelogram
Answers
Step-by-step explanation:
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Given:
Points A(0,0), B(3,0), C(4,1), D(1,1)
To prove:
The given points forms a parallelogram
Calculation:
In a parallelogram, opposite sides are equal and parallel. Also opposite angles of a parallelogram are equal.
Distance between two points A(x₁y₁), B(x₂,y₂) is
D = √(x₂-x₁)²+(y₂-y₁)²
Distance between the points A(0,0), B(3,0)
=> D = √(3-0)²+(0-0)²
=> D = √9
=> D = 3 units
Distance between the points B(3,0), C(4,1)
=> D = √(4-3)²+(1-0)²
=> D = √2 units
Distance between the points C(4,1), D(1,1)
=> D = √(1-4)²+(1-1)²
=> D = √9
=> D = 3 units
Distance between the points D(1,1), A(0.0)
=> D = √(0-1)²+(0-1)²
=> D = √2 units
Length of AB = Length of CD
Length of BC = Length of AD
Opposite sides of the figure obtained by joing the points A, B, C, D are equal
Hence ABCD Is a parallelogram