Answer:
Option (3) is correct.
The coordinates of the vertices of the given isosceles trapezoid centered in the origin, with base 2a and OR=c are,
S(-a, 0) , Z(a, 0) , T(-b, c) and W(b, c)
Explanation:
Given an isosceles trapezoid centered in the origin, with base 2a and OR = c.
We have to find the coordinates of vertices of the given isosceles trapezoid.
Since O is at center then , coordinates of O (0,0).
And base SZ given to be 2a .
So SO = OZ
SO + OZ = SZ ⇒ 2 (SO) = 2a ⇒SO = a
Since point S lies in second quadrant and x coordinates in second quadrant are negative, thus Coordinate of S is (-a, 0)
and Z lies in first quadrant , both x and y are positive,
So, coordinate of Z is (a, 0)
given OR = c so R lies on y axis , so R has coordinate (0,c)
Since point T lies in second quadrant and x coordinates in second quadrant are negative, thus Coordinate of T is of the form (-x, c)
also, W lies in first quadrant , both x and y are positive. Thus, coordinate of W is of the form (x,c)
When we compare from the given options, we get possible value of x is b,
Thus, the coordinates of the vertices of the given isosceles trapezoid centered in the origin, with base 2a and OR=c are,
S(-a, 0) , Z(a, 0) , T(-b, c) and W(b, c)
Option (3) is correct.