Question

Which quadrant does `(-3, 4)` lie in?

Answer 1

The second one.
Quadrants are characterised by signs of coordinates. Both signs + mean QI, signs `-+` (what you have here) mean QII, both `-` mean QIII, and `+ -` mean QIV.
Why is it so? Quadrants divide the full circle of directions from the origin to desired point, into 4 equal parts. We start tracing direction from the positive abscissa by convention. So the first quarter-circle (in counterclockwise direction) covers the area where both coordinates are positive. Second quarter-circle then covers the area where first coordinate is negative and second coordinate positive, and so on.