In the rectangle shown below, the sides are parallel to the axes and origin is the midpoint:

What are the coordinates of the other three vertices?

Since, O is the midpoint of the rectangle and sides of the rectangle are parallel to coordinate axis,

The rectangle is symmetrical about both X and Y axis.

Line AB is parallel to Y – axis,

∴ X coordinate will remain same

∴ X coordinate of B = 3

A is 2 units above X – axis , therefore by symmetry B will be 2 units below X – axis.

∴ Y coordinate of B = – 2

∴ coordinates of B = (3, – 2)

BC is parallel to the X axis

∴ Y coordinate will remain constant

∴ Y coordinate of C = – 2

B is 3 units right to the Y axis,

∴ by symmetry C will be 3 units to left of Y – axis.

∴ X coordinate of C = – 3

∴ coordinates of C = (– 3, – 2)

CD is parallel to Y – axis,

∴ X coordinate will remain constant

∴ X coordinate of D = – 3

The AD is parallel to X – axis,

∴ Y coordinate will remain constant

∴Y coordinate of D = 2

∴ coordinates of D = (– 3,2)

Hence, the coordinates of other three vertices are (3, – 2),(– 3, – 2)

And (– 3,2)