Question

Fill in the blanks to complete each of the following theorem statements:

A graph is symmetrical with respect to the origin if, for every point (r, θ) on the graph, the point ................is also on the graph.

Short answer

The blank is filled by$\left(-r,\theta \right)$

Step-by-step solution

Step 1. Given information 

The graph is symmetrical about y-axis for every point

 Step 2. Find the point.

As we know that the coordinates of the point $\left(r,\theta \right)$mean the distance of the point from origin is $r$and the angle made by positive x-axis is $\theta$.

A graph is symmetrical with respect to the origin if, for every point (r, θ) on the graph, the point $\left(-r,\theta \right)$ is also on the graph.