Write whether the following statements are True or False. Justify your answer.
(i) Point \((3, 0)\) lies in the first quadrant.
(ii) Points \((1, -1)\) and \((-1, 1)\) lie in the same quadrant.
(iii) The coordinates of a point whose ordinate is \(-\dfrac{1}{2}\) and abscissa is \(1\) are \((-\dfrac{1}{2}, 1)\).
(iv) A point lies on y-axis at a distance of 2 units from the x-axis. Its coordinates are \((2, 0)\).
(v) \((-1, 7)\) is a point in the II quadrant.
(i) False, because if ordinate of a point is zero, the point lies on the x-axis.
(ii) False. \((1, -1)\) lies in IV quadrant and \((-1, 1)\) lies in II quadrant.
(iii) False, because in the coordinates of a point abscissa comes first and then the ordinate.
(iv) False, because a point on the y-axis is of the form \((0, y)\).
(v) True, because in the II quadrant, signs of abscissa and ordinate are \(-\), \(+\), respectively.