Given, x+y=1....(i) 2x+3y=6....(ii) and 4x−y=−4....(iii) On solving Eqs. (i) and (ii), we get x=−3‌and‌y=4 Now, solving Eqs. (ii) and (iii), we get x=−
3
7
‌and‌y=
16
7
and solving Eqs. (i) and (iii), we get x=−
3
5
‌and‌y=
8
5
∴ Centroid of ∆ABC =[
x1+x2+x3
3
,
y1+y2+y3
3
] =[
(−3)+(−
3
5
)+(−
3
7
)
3
,
4+
8
5
+
16
7
3
] =[−
141
105
,
276
105
]≣(−x,y) Hence, the centroid lies in II quadrant.