Q. 26 A4.7( 6 Votes )

# Show that the following points are the vertices of a square:

A(3, 2), B(0, 5), C(– 3, 2) and D(0, – 1)

Answer :

AB = √{(0 – 3)^{2} + (5 – 2)^{2}} = √{9 + 9} = √18 units

BC = √{(– 3 – 0)^{2} + (2 – 5)^{2}} = √{9 + 9} = √18 units

CD = √{(0 – (– 3))^{2} + (– 1 – 2)^{2}} = √{9 + 9} = √18 units

DA = √{(0 – 3)^{2} + (– 1 – 2)^{2}} = √{9 + 9} = √18 units

AC = √{(– 3 – 3)^{2}} = √36 = 6 units

BD = √{(– 1 – 5)^{2}} = √36 = 6 units

Since AB = BC = CD = DA and AC = BD

∴ ABCD is a square.

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