show that (-2,1) ; (0, 3) , (2, 1) and (0, 1) are the vertices of a parallelogram
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Step-by-step explanation:
If the points are P(x
1
,y
1
) and Q(x
2
,y
2
), the slope of the line joining PQ is
x
2
−x
1
y
2
−y
2
For points, A(−2,1),B(0,3),C(2,1) and D(0,−1),
Slope of AB=
0+2
3−1
=1
Slope of BC=
2−0
1−3
=−1
Slope of CD=
0−2
−1−1
=1
Slope of DA=
0+2
−1−1
=−1
Clearly slope of AB= Slope of CD, hence, AB∥CD.
Clearly slope of BC= Slope of DA, hence, BC∥DA.
Since, the set of opposite sides are parallel to each other.
Thus, □ABCD are the vertices of a parallelogram
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