Question

a point is graphed in rectangular form. find polar coordinates for the point, with r > 0 and 0 ≤ θ < 2π. (r, θ) = ( )

Explanation:

Step1: Identify Rectangular Coordinates

The point \( Q \) is on the \( y \)-axis, below the origin. From the graph, the rectangular coordinates \((x, y)\) are \((0, -4)\) (assuming each grid square is 1 unit; counting down from the origin, 4 units).

Step2: Calculate \( r \)

Use the formula \( r = \sqrt{x^2 + y^2} \). Substituting \( x = 0 \), \( y = -4 \):
\( r = \sqrt{0^2 + (-4)^2} = \sqrt{16} = 4 \) (since \( r > 0 \)).

Step3: Determine \( \theta \)

For a point on the negative \( y \)-axis, the angle \( \theta \) (in standard position) is \( \frac{3\pi}{2} \) (or \( 270^\circ \)), as \( 0 \leq \theta < 2\pi \).

Answer:

\((4, \frac{3\pi}{2})\)