Question

Which could the coordinates of the vertices of the following isosceles trapezoid centered in the origin, with base 2a and OR=c?

Answer 1

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)

Step-by-step 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.