# Coordinate Geometry-14

### From Homeworkwiki

**Find the rectangular and polar coordinates of the vertices of a square ABCD with diagonal of 8 units. **

**[Take AB as the positive x-axis and AD as the positive y-axis]**

**Solution:** Let AB = BC = x

AB^{2} + BC^{2} = AC^{2}

2 x^{2} = 64

Therefore, x^{2} = 32

x = √32 = √ (16 x 2) = 4 √2

The coordinates of A, B, C, D in Cartesian rectangular coordinates are

A = (0, 0); B = (4√2, 0); C = (4√2, 4√2); D = (0, 4√2)

In polar coordinates, coordinates of A, B, C, D are

A = (0, 0); B = (4√2, 0); C = (8, 45^{0}); D = (4√2, 90^{0})