Question

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

A(2, 1), B(2, 5), D(–2, 1)

Answer 1

In coordinate geometry, to find the fourth vertex C(x, y) of a square ABCD given three vertices A(2, 1), B(2, 5) and D(–2, 1):

1. Identify the vertices: Points A and B are on the same vertical line (x = 2) and points A and D are on the same horizontal line (y = 1).

2. Determine the side length: The distance AB = |5 – 1| = 4 units and AD = |2 – (–2)| = 4 units.

3. Find vertex C: Since ABCD is a square, vertex C must be 4 units horizontally from B and 4 units vertically from D.

1. The x-coordinate of C is the same as D, which is –2. 
2. The y-coordinate of C is the same as B, which is 5.

Thus, the coordinates of the fourth vertex are C(–2, 5).