The shape of the given quadrilateral is given by plotting the given points
on a graph paper.
The correct response;
The given points are;
(0, 0), (1, 3), (5, 0), (6, 3)
The quadrilateral is therefore;
A(0, 0), B(1, 3), C(5, 0), D(6, 3)
Distance formula is d = √((x₂ - x₁)² + (y₂ - y₁)²)
The lengths of the sides are;
AB = √((1 - 0)² + (3 - 0)²) = √(10)
BC = √((5 - 1)² + (0 - 3)²) = 5
CD = √((6 - 5)² + (3 - 0)²) = √(10)
AD = √((6 - 0)² + (3 - 0)²) = 3·√5
However, by plotting the points, we have;
E(0, 0), F(1, 3), G(6, 3), H(5, 0)
Which gives;
EF = √(10)
FG = √( (6 - 1)² + (3 - 3)²) = 5
GH = √((5 - 6)² + (0 - 3)²) = √10
EH = 5
Therefore, the opposite sides are equal
EF = GH
FG = EH
Slope of EF = (3)/(1) = 3
Slope of GH = (3 - 0)/(6 - 5) = 3
Slope of FG = (3 - 3)/(6 - 1) = 0
Slope of EH = (0 - 0)/(5 - 0) = 0
Therefore, the slope of the opposite sides are equal, and the opposite
sides are parallel.
The slopes of the adjacent side are not the negative inverse of the other.
Therefore, the quadrilateral is a parallelogram
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