Straight Line Question 155

Question: Let A, (2,-3) and B (-2, 1) be the 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

Options:

A) $ 2x+3y=9 $

B) $ 2x-3y=7 $

C) $ 3x+2y=5 $

D) $ 3x-2y=3 $

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Answer:

Correct Answer: A

Solution:

  • [a] Let (x, y) be the coordinates of the vertex C and $ (x_1,y_1) $ be the coordinates of the centroid of the triangle. Therefore, $ x_1=\frac{x+2-2}{3} $ $ y_1=\frac{y-3+1}{3} $ Or $ x_1=\frac{x}{3} $ And $ y_1=\frac{y-2}{3} $ The centroid lies on the line $ 2x+3y=1 $ , so $ x_1 $ and $ y_1 $ satisfy the equation of the line. Thus $ 2x_1+3y_1=1 $

$ \Rightarrow 2( \frac{x}{3} )+3( \frac{y-2}{3} )=1 $

$ \Rightarrow 2x+3y=9 $ The above equation is the locus of the vertex c.