Question

Show that the points A(1,2) ,B(4,3), C(1,0) and D(-2,-1) are the vertices of a parallelogram.​

Answer 1

Answer:

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Given points are

A(−2,−1),B(1,0),C(4,3) and D(1,2)

A quadrilateral is a parallelogram if the opposite sides are equal.

∴AB^2 =(−2−1)^2 + (−1−0)^2

=9+1=10

BC^2 =(4−1)^2 + (3−0)^2

=9+9=18

CD^2 =(1−4)^2 + (2−3)^2

9+1=10

AD^2 =(−2−1)^2 + (−1−2)^2

=9+9=18

∴ The opposite sides of the quadrilateral ABCD are equal, the four points from a parallelogram.

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