Show that the points A(2, 1), B(5, 2), C(6, 4) and D(3, 3) are the angular points of a parallelogram. Is this figure a rectangle ?
Let A(2,1), B(5,2), C(6,4) and D(3,3) be the vertices of a parallelogram
ABCD. Since, the diagonals of a parallelogram bisect each other.AC2=(6−2)2+(4−1)2
=(4)2+(3)2
=16+9=25
BC2=(6−5)2+(4−2)2
=(1)2+(2)2
=1+4=5
AB2=(5−2)2+(2−1)2
=(3)2+(1)2=9+1=10
DC2=(6−3)2+(4−3)2
=(3)2+(1)2
=9+1=10
AD2=(3−2)2+(3−1)2
=(1)2+(2)2
=1+4=5
Since BC=AD and DC=AB, ABCD is a parallelogram.
AB2+BC2=10+5=15
AB2+BC2≠AC2
∴ΔABC is not right angled. Therefore parallelogram ABCD is not a rectangle.