In each of the following the co-ordinates of the three vertices of a rectangle ABCD are given. By plotting the given points, find, in each case, the co-ordinates of the fourth vertex:
`A(2,0),B(8,0)` and `C(8,4)`

Answer

To find the coordinates of the fourth vertex D of the rectangle ABCD given the coordinates of points A, B, and C, we can follow these steps:

### Step 1: Plot the Given Points
We have the following coordinates:
- A(2, 0)
- B(8, 0)
- C(8, 4)

Plot these points on a Cartesian plane:
- Point A is at (2, 0), which is 2 units to the right of the origin on the x-axis.
- Point B is at (8, 0), which is 8 units to the right of the origin on the x-axis.
- Point C is at (8, 4), which is 8 units to the right and 4 units up from the origin.

### Step 2: Identify the Rectangle's Structure
From the plotted points:
- Points A and B are on the same horizontal line (y = 0), indicating that they are on the base of the rectangle.
- Point C is directly above point B, which indicates that the rectangle's height extends vertically from point B to point C.

### Step 3: Determine the Fourth Vertex D
Since ABCD is a rectangle, the opposite sides are equal and parallel. We can find the coordinates of point D by observing that:
- The x-coordinate of D will be the same as that of A (since D is vertically aligned with A).
- The y-coordinate of D will be the same as that of C (since D is horizontally aligned with C).

Thus, the coordinates of point D will be:
- D(2, 4)

### Step 4: Finalize the Coordinates
The coordinates of the fourth vertex D of the rectangle ABCD are:
- D(2, 4)

### Summary
The coordinates of the fourth vertex D are (2, 4).

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