Question

Let A (2, -3) and B(-2, 1) 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) 2x + 3y = 9
(B) 2x – 3y = 7
(C) 3x + 2y = 5
(D) 3x – 2y = 3​

Answer 1

Answer:

Please see the attachment

Answer 2

the locus of the vertex C is the line 2x + 3y = 9

Step-by-step explanation:

A (2, -3) and B(-2, 1)

Let C is ( x , y)

Centroid  =  (2 + (-2) + x)/3  , (-3 + 1 + y)/3

= x/3  ,  (y - 2)/3

Centroid lies on 2x + 3y = 1

=> 2(x/3)  + 3(y - 2)/3 = 1

=> 2x  + 3y - 6 = 3

=> 2x + 3y = 9

the locus of the vertex C is the line 2x + 3y = 9

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