Question

show that (2,4) ,(2,-1),(-3,-1) and (3,4) are the vertices of the square.
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Answer 1

Let A(2,4),B(2,-1),C(-3,-1) and D(3,4).

Therefore by distance formula,

AB = √(2-2)^2 + [4-(-1)]^2 = √(5)^2 = 5 units

BC = √[2-(-3)]^2 + [-1-(-1)]^2 = √(5)^2 = 5 units

CD = √[-3 -3]^2 + [-1 -4]^2 = √(-6)^2 + (-5)^2 = √61 units

AD = √[2-3]^2 + [4-4]^2 = √(-1)^2 = 1 unit

Here, we see that AB = BC but CD = AD.

Thus, ABCB is not a square . [ since in a square, all sides should be equal]

Hope this helps you...