Question

Points in Polar Coordinates Determine which point in the figure,$P,Q,R\&S$ , has the given polar coordinates$(-4,-\frac{\pi }{4})$

Short answer

The respective point is Q

Step-by-step solution

Step 1. Given information

A point in polar coordinates as $(-4,-\frac{\pi }{4})$

Step 2. Concept used

The radius of the point in the polar coordinate system is the same. The only variation is the angle's value. So, if the angle value corresponds to the specified points, that point is the solution.

Step 3. Calculation

The given point is,$(-4,-\frac{\pi }{4})$

$\begin{array}{l}r=-4\\ \theta =-\frac{\pi }{4}\end{array}$

As a consequence, the outcome will be the inverse of the line segment of length 4 from the origin in the clockwise direction with an angle of$\frac{\pi }{4}$pi from thex axis.

As a result, the point Q is the one that meets the aforementioned requirements for the outcome.