ExamBro
ExamBro
TS EAMCET · Maths · Straight Lines

If the lines \(3 x+y-4=0, x-a y-10=0\), \(b x+2 y+9=0\) form three successive sides of a rectangle in that order and the fourth side passes through \((1,2)\), then the area of that rectangle (in sq. units) is

  1. A 8
  2. B \(\frac{15}{\sqrt{10}}\)
  3. C \(\frac{51}{\sqrt{40}}\)
  4. D \(\frac{51}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{51}{4}\)

Step-by-step Solution

Detailed explanation

Let rectangle be \(A B C D\). Here line \(A B \| C D\) \(\Rightarrow\) slope of line \(A B=\) slope of line \(C D\) \(\Rightarrow \quad-3=\frac{-b}{2} \Rightarrow b=6\) Now line \(A B \perp^r B C\) \(\Rightarrow(\) slope of line \(A B) \times(\) slope of line \(B C)=-1\)…