We have this rule for quadrant and sign of coordinate:
Quadrant I : x positive and y positive
Quadrant II : x negative and y positive
Quadrant III: x negative and y negative
Quadrant IV: x positive and y negative
let us check which of the points lies in quadrant III
A (-2,-2) , B(3,9) , C(-5,1) and D(1,-4)
here x and y both are negative for point A
so point A(-2,-2) lies in third quadrant.