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(-4,-6),C(6,0) and D(-4,0)

Answer

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

### Step 1: Plot the Given Points
We have the following coordinates:
- A(-4, -6)
- C(6, 0)
- D(-4, 0)

Let's plot these points on a Cartesian plane.

1. **Point A**: Locate -4 on the x-axis and -6 on the y-axis. This gives us point A at (-4, -6).
2. **Point C**: Locate 6 on the x-axis and 0 on the y-axis. This gives us point C at (6, 0).
3. **Point D**: Locate -4 on the x-axis and 0 on the y-axis. This gives us point D at (-4, 0).

### Step 2: Identify the Rectangle
Since we know that ABCD is a rectangle, we can identify the sides:
- Side AD is vertical (from A to D).
- Side CD is horizontal (from C to D).

### Step 3: Draw Perpendicular Lines
To find the fourth vertex B, we need to extend perpendicular lines from points A and C:
1. Draw a horizontal line from point A to the right.
2. Draw a vertical line from point C downwards.

### Step 4: Find the Intersection Point
The intersection of these two lines will give us the coordinates of point B:
- The horizontal line from A will be at y = -6.
- The vertical line from C will be at x = 6.

### Step 5: Determine the Coordinates of B
The coordinates of point B can be determined as follows:
- Since the vertical line from C is at x = 6 and the horizontal line from A is at y = -6, the coordinates of point B will be (6, -6).

### Conclusion
Thus, the coordinates of the fourth vertex B are (6, -6).

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