Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two vertices.

Question

Philoid · Accepted Answer

The coordinates are A(-1, 2) and C(3, 2).

Let the coordinates of the vertex B are (x, y)

AB = BC

Using distance formula =

On squaring both sides, we get

=

In ΔABC

AB² + BC² = AC² [Using Pythagoras theorem]

2AB² = AC² [Since AB = BC]

=

= 16

= 8

= 3

On substituting x = 1

= 3

= 0

= 0, 4

Other coordinates are (1, 0) and (1, 4)