Question

With the axes of coordinates chosen along two adjacent sides of a rectangle, two opposite vertices have coordinates (0, 0) and (4, 3). What are the coordinates of the other two vertices?

Answer 1

If the coordinate axes are chosen along the two adjacent sides of a rectangle with two opposite vertices having coordinates (0, 0) and (4, 3), then the rectangle can be drawn as follows:

As ABCO is a rectangle.

∴ AB = OC and BC = AO

The coordinates of point B are (4, 3).

Therefore, the perpendicular distance of point B from the x-axis and y-axis is 3 units and 4 units respectively.

Point A of the given rectangle lies on y-axis. Therefore, its x-coordinate is 0.

Also, the perpendicular distance of point A from the origin = Perpendicular distance of point B from the x-axis = 3 units.

Therefore, the x-coordinate of point A is 0 and the y-coordinate is 3.

So, the coordinates of point A are (0, 3).

Point C of the given rectangle lies on the x-axis. Therefore, its y-coordinate is 0.

The perpendicular distance of point C from the origin = Perpendicular distance of point B from the y-axis = 4 units.

Therefore, the x-coordinate of point C is 4 and the y-coordinate is 0.

So, the coordinates of point C are (4, 0).

Thus, the coordinates of the other two vertices of the given rectangle are (0, 3) and (4, 0).