Answer
a. $(-3,3)$
b. $3\sqrt{2}$
c. $-225^{\circ}$
Work Step by Step
a.
The terminal side of $135^{\circ}$ in standard position is in the 2nd. It lies along the line $y=-x$ where the $x$ coordinate is negative and the $y$ coordinate is positive. The terminal side is represented by the blue line in the figure.
The coordinates of points on the terminal side of $135^{\circ}$ 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 $135^{\circ}$, we traverse a full revolution in the positive or negative direction.
Negative coterminal angle = $135^{\circ}-360^{\circ}= -225^{\circ}$
