# Show that the points (1, 7), (4, 2), (–1, –1) and (– 4, 4) are the vertices of a square.

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by chetanKunda

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by chetanKunda

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Let the points are A,B,C,D.

Distance formula = √(x₂-x₁)²+(y₂-y₁)²

AB = √(4-1)²+(2-7)²

= √9+25

= √34

BC = √(-1-4)²+(-1-2)²

= √25+9

= √34

CD = √(-4-(-1))²+(4-(-1))²

= √9+25

= √34

DA = √(1-(-4))²+(7-4)²

= √25+9

= √34

We know that the all sides of the square are equal.

Here by the distance formula, we got the for sides equal .

So,from this we can say that these points are the vertices of a square.