ExamBro
ExamBro
AP EAMCET · Maths · Straight Lines

\(\mathrm{A}(3,-4)\) is a vertex of \(\triangle \mathrm{ABC}\) and \(3 x+4 y-18=0\) is the perpendicular bisector of the side \(\mathrm{AB}\). If \(\mathrm{C}=(6,3)\) then the centroid of the triangle is

  1. A \((6,1)\)
  2. B \((-6,1)\)
  3. C \((-6,-1)\)
  4. D \((6,-1)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \((6,1)\)

Step-by-step Solution

Detailed explanation

Point B is the reflection of A across the line \(3x+4y-18=0\). \(\frac{x_B - 3}{3} = \frac{y_B - (-4)}{4} = -2 \frac{3(3) + 4(-4) - 18}{3^2 + 4^2}\) \(\frac{x_B - 3}{3} = \frac{y_B + 4}{4} = -2 \frac{-25}{25} = 2\) \(x_B = 3 + 3(2) = 9\) \(y_B = -4 + 4(2) = 4\) \(B = (9,4)\)…