The points A(3, 2) B(0, 5) and D(0, - 1) are the three vertices of a square ABCD. Plot these points on a graph paper and hence find the co-ordinates of the vertex C.
The points A(2, - 2) B(8, 4) and C(5, 7) are three vertices of a rectangle ABCD. Plot these points on a graph paper and hence, find the co-ordinates of its fourth vertex D.
Show that the points A (1, 2), B (5, 4), C (3, 8) and D (-1, 6) are the vertices of a square. [Hint.Show that AB = BC = CD = DA and diag. AC = diag. BD.]
Show that the points A (1, 1), B (-1, 5), C (7, 9) and D (9, 5) are the vertices of a rectangle ABCD. [Hint. Show that AB = CD, BC = AD and diag. AC = diag. BD.]
Find the point on the y-axis, which is equidistant from the points A(- 3, 2) and B (5, -2). $\left[\right.$ Hint . Let the required point be $P (0, y)$. Then, $AP = BP \Rightarrow AP ^2= BP ^2$.]
Find the point on the x-axis, which is equidistant from the points A(2, - 5) and B (-2, 9). [Hint . Let the required point be $P (x, 0)$. Then $\left.AP = BP \Rightarrow AP ^2= BP ^2\right]$