Show that the points (1,7),(4,2),(-1,-1),(-4,4) are the vertices of a square?

Show that the points (1,7),(4,2),(-1,-1),(-4,4) are the vertices of a

1.	Show that the points (1,7),(4,2),(-1,-1),(-4,4) are the vertices of a square?
Answer» Given points are (1,7),(4,2),(-1,-1),(-4,4)Let the points are A,B,C,D.Distance formula =\xa0√(x₂-x₁)²+(y₂-y₁)² AB =\xa0√(4-1)²+(2-7)² =\xa0√9+25 =\xa0√34 BC =\xa0√(-1-4)²+(-1-2)² =\xa0√25+9 = √34 CD =\xa0√(-4-(-1))²+(4-(-1))² =\xa0√9+25 = √34 DA =\xa0√(1-(-4))²+(7-4)² =\xa0√25+9 =\xa0√34\tWe 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.