Question

In the following, three vertices of a rectangle are given. Plot these points on a graph paper and find the co-ordinates of the fourth vertex:

A(2, 0), B(2, 3), C(–4, 3)

Answer 1

To find the fourth vertex of the rectangle ABCD with the given points A(2, 0), B(2, 3) and C(–4, 3), we analyze the properties of a rectangle.

1. Identify the orientation of the sides

A rectangle has sides that are perpendicular to each other and parallel to the coordinate axes if the vertices share coordinate values.

Segment AB: The x-coordinates are the same (x = 2). Therefore, AB is a vertical segment. 

Segment BC: The y-coordinates are the same (y = 3). Therefore, BC is a horizontal segment.

2. Determine the fourth vertex (D)

For ABCD to be a rectangle, the remaining sides must also be horizontal and vertical:

Side CD must be a vertical segment starting from C(–4, 3). This means point D must have the same x-coordinate as C, which is –4.

Side AD must be a horizontal segment starting from A(2, 0). This means point D must have the same y-coordinate as A, which is 0.

Combining these, the coordinates of D are (–4, 0).

3. Graphical representation

The points are plotted below to complete the rectangle:

The coordinates of the fourth vertex are D(–4, 0).