Question

In the figure below, ABCD is a rectangle with the origin O as its centre and sides parallel to the axis.

What are the coordinates of B, C, D?

Answer 1

Given: ABCD is a rectangle with sides parallel to the axes.

∴ AB = DC and BC = AD

It can be observed that the coordinate axes have divided the given rectangle into four congruent rectangles.

The coordinates of point A are (3, 2).

Therefore, the perpendicular distance of point A from x-axis and y-axis is 2 units and 3 units respectively.

Thus, the perpendicular distance of point B, point C, and point D from x-axis and y-axis would be 2 units and 3 units respectively.

Point B lies in the second quadrant.

Therefore, the x-coordinate of point B is −3 and the y-coordinate is 2.

So, the coordinates of point B are (−3, 2).

Point C lies in the third quadrant.

Therefore, the x-coordinate of point C is −3 and the y-coordinate is −2.

So, the coordinates of point C are (−3, −2).

Point D lies in the fourth quadrant.

Therefore, the x-coordinate of point D is 3 and the y-coordinate is −2.

So, the coordinates of point D are (3, −2).