Question

Q. Let A(2, - 3) and B(-2, 3) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line
A 3x - 2y = 3
B 2x -3y = 7
C 3x + 2y = 5
D 2x + 3y = 9

Answer 1

Step-by-step explanation:

ANSWER

Let (h,k) be the coordinates of the centroid of ∆ABC.

Thus 3h=cosa+sina+1 and 3k=sina−cosa+2

⇒(3h−1)

2

+(3k−2)

2

=2

Hence locus of (h,k) is

(3x−1)

2

+(3y−2)

2

=2

9x

2

+9y

2

−6x−12y+3=0

3x

2

+3y

2

−2x−4y+1=0

#khushu☺️