Question

47. Let ABC be an equilateral triangle. If the co-
ordinates of A are (1, 2) and co-ordinate of B
are(2,-1), then
(1) C cannot lie in the first quadrant
(2) C cannot lie in the second quadrant.
(3) C is the origin
(4) C cannot lie in the third quadrant​

Answer 1

Answer:

2) C cannot lie in the second quadrant

(x−1)2+(y−2)2=(x−2)2+(y+1)2⇒2x−6y=0⇒x=3y

(1−2)2+(2+1)2=(x−1)2+(y−2)2

1+9=x2+1−2x+y2+4−4y⇒x2+y2−2x−4y−5=0

9y2+y2−(3y)−4y−5=0

2y2−2y−1=0⇒y=42±4+8=21±23⇒y=1±3

∴C(3+33