TS EAMCET · Maths · Straight Lines
If \(A(2,-3)\) and \(B(-2,1)\) are two vertices of a triangle and third vertex moves on the line \(2 x+3 y=9\), then the locus of the centroid of the triangle is
- A \(2 x-3 y=1\)
- B \(x-y=1\)
- C \(2 x+3 y=1\)
- D \(2 x+3 y=3\)
Answer & Solution
Correct Answer
(C) \(2 x+3 y=1\)
Step-by-step Solution
Detailed explanation
Given \(A(2,-3) B(-2,1)\) The third vertex lies on \(2 x+3 y=9\) i.e. \(C\left(x, \frac{9-2 x}{3}\right)\) \(\therefore\) Let \(P(h, k)\) be any point on the required locus i.e \(P\) is the centroid of the triangle \(A B C\)…
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