A square with sides of length a and a center at the origin has two sides parallel to the​ x-axis. Find the polar coordinates of the vertices. Choose the correct answer below. Select all that apply.

Question

A square with sides of length a and a center at the origin has two sides parallel to the​ x-axis. Find the polar coordinates of the vertices. Choose the correct answer below. Select all that apply.

Answer 1

Pretty easy to see that each vertex is a/2 away from the origin in both the x-direction and the y-direction and that each is at a 45° angle.

The polar coordinates are in the form of (r, θ) where "r" is the distance from the origin. Calculate "r" using the Pythagorean Theorem:

(a/2)² + (a/2)² = r²

r = √(a²/4 + a²/4) = √(a²/2) = a/√2 = a√2/2

This will be the same value of "r" for all 4 vertices.

For the vertex in quadrant I, θ = π/4 which makes to polar coordinate: (a√2/2, π/4)

For the vertex in Q II, θ = 3π/4

For the vertex in Q III, θ = 5π/4

For the vertex in Q IV, θ = 7π/4