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TS EAMCET · Maths · Straight Lines

In the triangle with vertices at \(A(6,3), B(-6,3)\) and \(C(-6,-3)\), the median through \(A\) meets \(B C\) at \(P\), the line \(A C\) meets the \(x\)-axis at \(Q\), while \(R\) and \(S\) respectively denote the orthocentre and centroid of the triangle. Then the correct matching of the coordinates of points in List-I to List-II is \(\begin{array}{llll} & \text { List-I } & & \text { List-II } \ \text { (i) } & P & \text { (A) } & (0,0) \ \text { (ii) } & Q & \text { (B) } & (6,0) \ \text { (iii) } & R & \text { (C) } & (-2,1) \ \text { (iv) } & S & \text { (D) }(-6,0) \ & & \text { (E) }(-6,-3) \ & & \text { (F) }(-6,3)\end{array}\) (i) (ii) (iii) (iv)

  1. A \(\begin{array}{llll}\mathrm{D} & \mathrm{A} & \mathrm{E} & \mathrm{C}\end{array}\)
  2. B \(\begin{array}{llll}\mathrm{D} & \mathrm{B} & \mathrm{E} & \mathrm{C}\end{array}\)
  3. C \(\begin{array}{llll}\text { D } & \text { A } & \text { F } & \text { C }\end{array}\)
  4. D \(\begin{array}{llll}\text { B } & \text { A } & \text { F } & \text { C }\end{array}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\begin{array}{llll}\text { D } & \text { A } & \text { F } & \text { C }\end{array}\)

Step-by-step Solution

Detailed explanation

\(A(6,3), B(-6,3), C(-6,-3)\) forms a right angled triangle. In which \(\angle B=90^{\circ}\) Equation of \(A C\) is \(y-3=\frac{-3-3}{-6-6}(x-6)\)…