Determine the coordinate of R

You're on a roll — let's determine the coordinates of R:

Step 1: From the diagram, point R lies on the x-axis. This means its y-coordinate is $0$. So, the coordinates of R can be written as $(x_R, 0)$.

Step 2: Point R also lies on the line QR, whose equation is given as $x + 3y + 6 = 0$. Substitute $y = 0$ into this equation to find $x_R$. $x_R + 3(0) + 6 = 0$ $x_R + 0 + 6 = 0$ $x_R + 6 = 0$ $x_R = -6$

Step 3: Combine the x and y coordinates to state the coordinates of R. The coordinates of R are $\boxed{(-6, 0)}$.

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