Coordinate Geometry-14

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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

AB² + BC² = AC²

2 x² = 64

Therefore, x² = 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, 45⁰); D = (4√2, 90⁰)