Question

In the figure below, ABCD is a square. Find the coordinates of B, C, D.

Answer 1

It is given that ABCD is a square.

We know that diagonals of a square are equal and are perpendicular bisectors of each other.

∴ AO = BO = DO = CO

The coordinates of point A are (2, 0).

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

∴ AO = 2 units

⇒ BO = DO = CO = 2 units

As the length of BO is 2 units, the y-coordinate of point B is 2.

Also, as point B is lies on the y-axis, the x-coordinate of point B is 0.

So, the coordinates of point B are (0, 2).

As the length of CO is 2 units and point C lies on the negative x-axis, the x-coordinate of point B is −2.

Also, as point C is lies on the x-axis, the y-coordinate of point C is 0.

So, the coordinates of point C are (−2, 0).

As the length of DO is 2 units and point D lies on the negative y-axis, the y-coordinate of point D is −2.

Also, as point D lies on y-axis, the x-coordinate of point D is 0.

So, the coordinates of point D are (0, −2).