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:
B(10,4),C(0,4) and D(0,-2)

Answer

To find the coordinates of the fourth vertex A of rectangle ABCD given the coordinates of vertices B(10, 4), C(0, 4), and D(0, -2), we can follow these steps:

### Step-by-Step Solution:

1. **Plot the Given Points**:
- Plot point B(10, 4) on the Cartesian plane. This point is located 10 units along the x-axis and 4 units up on the y-axis.
- Plot point C(0, 4). This point is located on the y-axis, 4 units up.
- Plot point D(0, -2). This point is also on the y-axis, but 2 units down.

2. **Connect the Points**:
- Connect points B and C with a horizontal line. Since both points have the same y-coordinate (4), they form the top side of the rectangle.
- Connect points C and D with a vertical line. Since both points have the same x-coordinate (0), they form the left side of the rectangle.

3. **Extend Lines to Find Fourth Vertex**:
- Extend a vertical line downwards from point B(10, 4). This line will run parallel to the y-axis.
- Extend a horizontal line to the right from point D(0, -2). This line will run parallel to the x-axis.

4. **Find the Intersection Point**:
- The intersection of the vertical line from B and the horizontal line from D will give us the coordinates of point A.
- The x-coordinate of point A will be the same as that of point B, which is 10.
- The y-coordinate of point A will be the same as that of point D, which is -2.

5. **Conclusion**:
- Therefore, the coordinates of the fourth vertex A are (10, -2).

### Final Answer:
The coordinates of the fourth vertex A are (10, -2).