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(1, 1), В(1, 4), С(4, 4)

Answer 1

To find the coordinates of the fourth vertex D(x, y) for the square ABCD, we follow these steps:

1. Plot the given points:

A(1, 1): Located in the first quadrant, 1 unit from the y-axis and 1 unit from the x-axis.

B(1, 4): Located directly above point A because they share the same x- coordinate. The vertical distance AB is 4 – 1 = 3 units.

C(4, 4): Located to the right of point B because they share the same y- coordinate. The horizontal distance BC is 4 – 1 = 3 units.

2. Determine the position of D:

In a square ABCD, all sides are equal and adjacent sides are perpendicular.

Since AB is a vertical line segment and BC is horizontal, the side CD must be a vertical line segment starting from C(4, 4).

To maintain a side length of 3 units, we move 3 units down from C(4, 4).

The x-coordinate remains 4 and the y-coordinate becomes 4 – 3 = 1.

This gives us the point D(4, 1).

3. Verify the properties:

The side DA connects D(4, 1) and A(1, 1). This is a horizontal line with a length of 4 – 1 = 3 units. 

Since all sides are 3 units long and the angles are 90°, ABCD is indeed a square.

The coordinates of the fourth vertex are D(4, 1).