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  • Let A( -3,2 ) and B( -2,1 ) be the vertices of a triangle ABC. If the centroid of this triangle lies on the line <img alt="3x+4y+2=0" src="http://entrancecorner.oncodecogs.

Let A( -3,2 ) and B( -2,1 ) be the vertices of a triangle ABC. If the centroid of this triangle lies on the line 3x+4y+2=0,t hen the vertex C lies on the line :

Option: 1

4x+3y+5=0


Option: 2

3x+4y+3=0


Option: 3

4x+3y+3=0


Option: 4

3x+4y+5=0


Answers (1)

best_answer

Let C = (x1, y1)

\text { Centroid, } \mathrm{E}=\left(\frac{x_{1}-5}{3}, \frac{y_{1}+3}{3}\right)

since, centroid lies on the line 3x + 4y + 2 = 0

\therefore \quad 3\left(\frac{x_{1}-5}{3}\right)+4\left(\frac{y_{1}+3}{3}\right)+2=0

\\\Rightarrow \quad 3 x_{1}+4 y_{1}+3=0 \\\\ \text{Hence vertex }\left(x_{1}, y_{1}\right)\text{ lies on the line }3 x+4 y+3=0

Posted by

Rakesh

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