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TS EAMCET · Maths · Straight Lines

Two non parallel sides of a rhombus are parallel to the lines \(x+y-1=0\) and \(7 x-y-5=0\). If \((1,3)\) is the centre of the rhombus and one of its vertices \(\mathrm{A}(\alpha, \beta)\) lies on \(15 x-5 y=6\), then one of the possible values of \((\alpha+\beta)\) is

  1. A \(\frac{18}{5}\)
  2. B \(\frac{12}{5}\)
  3. C \(\frac{37}{5}\)
  4. D \(\frac{39}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{18}{5}\)

Step-by-step Solution

Detailed explanation

Slopes of diagonals are slopes of angle bisectors of \(x+y-1=0\) and \(7x-y-5=0\). \( \frac{x+y-1}{\sqrt{1^2+1^2}} = \pm \frac{7x-y-5}{\sqrt{7^2+(-1)^2}} \Rightarrow 5(x+y-1) = \pm (7x-y-5) \)…