Question

show that the points 1,7 4,2 -1,-1 and -4,4 are vertice of a square​

Answer 1

Answer:

We know that,

diagonals of a square bisect each other.

So,if mid point of diagonal AC is equal to mid point of diagonal BD,then ABCD is a parallelogram.

Then if it is proved that the diagonals are equal then ABCD is a rectangle.

And then,if it is proved that the adjacent sides are equal,then we are confirmed that the given points are vertices of square.

Midpoint of AC=1-1/2,7-1/2=0,3

Midpoint of BD=4-4/2,2+4/2=0,3

Since,the midpoints are equal.

Therefore,ABCD is a parallelogram.

AC=((-1-1)^2+(-1-7)^2)^1/2=(4+64)^1/2=68^1/2

BD=((-4-4)^2+(4-2)^2)^1/2=(64+4)^1/2=68^1/2

Since,the diagonals are equal,ABCD is a rectangle.

AB=((4-1)^2+(2-7)^2)^1/2=(9+25)^1/2=34^1/2.

BC=((-1-4)^2+(-1-2)^2)^1/2=(25+9)^1/2=34^1/2.

Since,the adjacent sides are equal,we are confirmed that the given points are vertices of square.

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