Answer
a. $(-3,-3)$
b. $3\sqrt{2}$
c. $-135^{\circ}$
Work Step by Step
a.
The terminal side of $225^{\circ}$ in standard position is in the 3rd quadrant. It lies along the line $y=x$ . The terminal side is represented by the blue line in the figure.
The coordinates of points on the terminal side of $225^{\circ}$ can be given by $(-a,-a)$, where $a$ is a positive number.
Choosing $a=3$ arbitrarily, the point is $(-3,-3)$.
b.
To find the distance from the origin to $(-3,-3)$, we use the distance formula
$$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(-3-0)^2+(-3-0)^2}=\sqrt{18}=\sqrt{9\times2}$$
$$\therefore r = 3\sqrt{2}$$
c.
To find an angle that is coterminal with $225^{\circ}$, we traverse a full revolution in the positive or negative direction.
Negative coterminal angle = $225^{\circ}-360^{\circ}= -135^{\circ}$
