AP EAMCET · Maths · Straight Lines
\(\mathrm{A}(2,3), \mathrm{B}(3,-5)\) are two vertices of \(\triangle \mathrm{ABC}\). If the centroid of the \(\triangle \mathrm{ABC}\) moves on the line \(2 x+y-2=0\), then the locus of \(\mathrm{C}\) is
- A \(x+2 y+2=0\)
- B \(2 x+y+2=0\)
- C \(2 x+y-2=0\)
- D \(3 x+y+2=0\)
Answer & Solution
Correct Answer
(B) \(2 x+y+2=0\)
Step-by-step Solution
Detailed explanation
Let C be \( (x, y) \). Centroid G \( \left( \frac{2+3+x}{3}, \frac{3-5+y}{3} \right) = \left( \frac{5+x}{3}, \frac{-2+y}{3} \right) \). Substitute G into \( 2x+y-2=0 \): \( 2\left(\frac{5+x}{3}\right) + \left(\frac{-2+y}{3}\right) - 2 = 0 \) \( 2(5+x) + (-2+y) - 6 = 0 \)…
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