Answer
$\color{blue}{\bf{\text{Quadrants 3, 1, 4, & 4 respectively}}}$
Work Step by Step
Remember that quadrants start at positive $x$ and $y$ values and run counter-clockwise:
$\bf{\text{Quadrant 1} = (+x, +y)}$
$\bf{\text{Quadrant 2} = (-x, +y)}$
$\bf{\text{Quadrant 3} = (-x, -y)}$
$\bf{\text{Quadrant 4} = (+x, -y)}$
If $\bf{(a,b)}$ is in $\bf\text{Quadrant 2}$, than it must be in the form:
$\bf{(−x,+y)}$
Therefore, $\bf{a}$ must be a$\bf{ \text{ negative }}$value,
and $\bf{b}$ must be a $\bf{ \text{positive }}$value
$\bf{(a,-b)}$ = $\bf{(-x,-y)}$ which is in $\color{blue}{\bf{\text{Quadrant 3}}}$
$\bf{(-a,b)}$ = $\bf{(x, y)}$ which is in $\color{blue}{\bf{\text{Quadrant 1}}}$
$\bf{(-a,-b)}$ = $\bf{(x, -y)}$ which is in $\color{blue}{\bf{\text{Quadrant 4}}}$
$\bf{(b,a)}$ = $\bf{(x, -y)}$ which is in $\color{blue}{\bf{\text{Quadrant 4}}}$
