Respuesta :
Answer:
To find the area of rectangle ABCD, we need to determine the coordinates of all four vertices first.
We know that the x-coordinate of point A is 2. Since all four vertices lie on the graph of y = 1/x, we can substitute x = 2 into the equation to find the y-coordinate of point A.
y = 1/x
y = 1/2
So, the coordinates of point A are (2, 1/2).
To find the coordinates of the other vertices, we can use the fact that a rectangle has opposite sides that are parallel and equal in length. Since the opposite sides of rectangle ABCD are vertical, they will have the same x-coordinate.
Since point A has an x-coordinate of 2, the opposite vertex D will also have an x-coordinate of 2.
Now, we can find the y-coordinate of point D by substituting x = 2 into the equation y = 1/x.
y = 1/2
So, the coordinates of point D are (2, 1/2).
Since the opposite sides of a rectangle are equal in length, the length of side AB is equal to the distance between the y-coordinates of points A and D, which is 1/2 - 1/2 = 0.
Similarly, the length of side AD is equal to the distance between the x-coordinates of points A and D, which is 0.
Therefore, the area of rectangle ABCD is 0.
