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BITSAT 2024Paper 1
Exam
BITSAT
Year
2024
Paper
Paper 1
Subject
Mathematics
Chapter
Straight Lines

BITSAT 2024 · Paper 1 · Mathematics · Straight Lines

The distance from the origin to the image of (1 , 1) with respect...

The distance from the origin to the image of (1(1, 1) with respect to the line x+y+5=0x+y+5=0 is

Options

  1. A727 \sqrt{2}
  2. B323 \sqrt{2}
  3. C626 \sqrt{2}
  4. D424 \sqrt{2}

Correct answer

C. 626 \sqrt{2}

Step-by-step solution

As we know that the image of (1,1)(1,1) with respect to line x+y+5=0x+y+5=0 is x−11=y−11=2(1+1+5)1+1⇒x−1=−7,y−1=−7⇒x=−6,y=−6∴\frac{x-1}{1}=\frac{y-1}{1}=\frac{2(1+1+5)}{1+1}\Rightarrow x-1=-7, y-1=-7\Rightarrow x=-6, y=-6\therefore \quad Image of point (1,1)(1,1) is (−6,−6)(-6,-6) Now, distance from origin This is the required transformed equation. D=(0+6)2+(0+6)2D=72=62D=\sqrt{(0+6)^2+(0+6)^2}D=\sqrt{72}=6 \sqrt{2}
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