Question

One vertex of a rectangle is at origin. Its two adjacent sides are along positive x-axis and along positive y-axis which are 4 units and 3 units respectively. Draw the rectangle on the graph paper and write the co-ordinates of its vertices.

Answer 1

1. Identify the first three vertices

Since one vertex is at the origin, the first coordinate is O(0, 0). The side along the positive x-axis has a length of 4 units, placing the second vertex at A(4, 0). The side along the positive y-axis has a length of 3 units, placing the third vertex at C(0, 3).

2. Determine the fourth vertex

In a rectangle, opposite sides are equal and parallel. To complete the shape from A(4, 0) and C(0, 3), we move 3 units up from A or 4 units right from C. This results in the fourth vertex B having an x-coordinate of 4 and a y-coordinate of 3, which is B(4, 3).

3. Verify the geometry

The distance between O(0, 0) and A(4, 0) is `sqrt((4 - 0)^2 + (0 - 0)^2` = 4 units.

The distance between O(0, 0) and C(0, 3) is `sqrt((0 - 0)^2 + (3 - 0)^2` = 3 units.

All adjacent sides are perpendicular, the shape is a rectangle.

The coordinates of the vertices of the rectangle are (0, 0), (4, 0), (4, 3) and (0, 3).