Question

Write the coordinates of vertices of a rectangle OABC, where O is the origin, length OA = 5 units lying along x-axis, breadth AB = 3 units and B lying in the fourth quadrant.

Answer 1

Given: OABC is a rectangle. O is the origin, OA = 5 units along the x-axis, AB = 3 units and B lies in quadrant IV.
Solution: Coordinates of origin, i.e., O = (0,0)
Point A lies on the x-axis. So, coordinates of point A = (5,0)
Point B lies in the fourth quadrant. So, ordinate of point B is negative.
As width AB = 3 units, coordinates of point B = ( 5,−3)
Point C and point O lies on the same line.
Hence, abscissa of C = abscissa of O = 0
It means that point C lies on the y-axis.
Similarly, point C and point B lie on the same altitude. So, the ordinates of both points must be equal.
i.e., ordinate of C = ordinate of B = (−3)
i.e., coordinates of C = (0, −3)
Thus, the coordinates of the vertices of rectangle OABC are O(0,0), A( 5,0), B( 5, -3) and C( 0,-3).