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

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3x + 2y = 5

2x – 3y = 7

2x + 3y = 9

3x – 2y = 3

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detailed solution

Correct option is C

Let C(h, k) be the vertex, then the centroid is h+2−23,k−3+13 i.e. (h/3, (k – 2)/3) which lies on 2x + 3y = 1 ⇒ 2h3+3(k−2)3=1⇒ 2h+3k=9 and the locus of (h, k) is 2x + 3y = 9

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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

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Ready to Test Your Skills?

free study material

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