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(4,2), B(-2,2) and D(4,-2)

Answer

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

### Step 1: Plot the Given Points
- Plot the points \( A(4,2) \), \( B(-2,2) \), and \( D(4,-2) \) on a coordinate plane.

### Step 2: Identify the Coordinates
- The coordinates are:
- \( A(4,2) \)
- \( B(-2,2) \)
- \( D(4,-2) \)

### Step 3: Draw Lines
- Draw a horizontal line between points \( A \) and \( B \) (both have the same \( y \)-coordinate of 2).
- Draw a vertical line between points \( D \) and \( A \) (both have the same \( x \)-coordinate of 4).

### Step 4: Determine the Fourth Vertex \( C \)
- Since \( AB \) is horizontal and \( AD \) is vertical, the fourth vertex \( C \) will be directly below \( B \) and directly to the left of \( D \).
- To find the coordinates of \( C \):
- The \( x \)-coordinate of \( C \) will be the same as \( B \), which is \( -2 \).
- The \( y \)-coordinate of \( C \) will be the same as \( D \), which is \( -2 \).

Thus, the coordinates of the fourth vertex \( C \) are \( C(-2,-2) \).

### Final Answer
The coordinates of the fourth vertex \( C \) are \( (-2, -2) \).

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