Coordinate Geometry Question 21
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
[AIEEE 2004]
Options:
A) $ 3x-2y=3 $
B) $ 2x-3y=7 $
C) $ 3x+2y=5 $
D) $ 2x+3y=9 $
Show Answer
Answer:
Correct Answer: D
Solution:
Let the third vertex be $ (x_1,y_1) $ then Centroid $ (G)\equiv ( \frac{x_1+2-2}{3},\frac{y_1-3+1}{3} ) $ i.e., $ G( \frac{x_1}{3},\frac{y_1-2}{3} ) $ Given, centroid of triangle moves on the line $ 2x+3y=1 $
$ \therefore $ $ 2( \frac{x_1}{3} )+3( \frac{y_1-2}{3} )=1 $ i.e., $ 2x_1+3y_1=9 $ Locus of $ (x_1,y_1) $ is $ 2x+3y=9 $ .
BETA
