Show that following points are vertices of a square: (0,1) , (1,4) , (4,3) , (3,0). Share with your friends Share 1 Varun.Rawat answered this Let A0,1; B1,4; C4,3; D3, 0 are the given points.Now, we know that distance between points x1, y1 and x2, y2 is given bydistance = x2 - x12 + y2 - y12Now, AB = 1-02 + 4-12 = 12 + 32 = 1+9 = 10 unitsNow, BC = 4-12 + 3-42 = 32 + -12 = 9+1 = 10 unitsNow, CD = 3-42 + 0-32 = -12 + -32 = 1+9 = 10 unitsNow, DA = 0-32 + 1-02 = -32 + 12 = 9+1 = 10 unitsNow, AC = 4-02 + 3-12 = 16 + 4 = 20 = 25 unitsNow, BD = 3-12 + 0-42 = 4+16 = 20 = 25 unitsSo, in quadrilateral ABCD, we have,AB = BC = CD = DA and AC = BDSo, given quadrilateral is a square.We know that a quadrilateral is a square, if each of its sides are equal and also its diagonals are equal. 0 View Full Answer Mohammed Ibrahim Dug answered this Expert please answer. -1 Rishabh Gupta answered this let these points form a quadrilateral ABCD here A ( 0,1) B (1,4) C ( 4,3) D ( 3,0) properties of a square = all sides are equal and all diagnols are equal length of side ab = root 10 ( by applying distance formula) length of side bc = root 10 ( by applying distance formula) length of side cd = root 10 ( by applying distance formula) length of side ad = root 10 ( by applying distance formula ) length of diagonal ac = root 20 ( by applying distance formula ) length of diagonal bd = root 20 ( by applying distance formula ) as all the sides and both the diagonals of the quadrilateral are equal , hence it is a square 2
