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9. straight line — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS9. straight line1 Mark
MCQ
Let $L$ be the line passing through the point $P( 1, 2)$ such that its intercepted segment between the co-ordinate axes is bisected at $P$. If $L_1$ is the line perpendicular to $L$ and passing through the point $(-2 , 1),$ then the point of intersection of $L$ and $L_1$ is
  • ✓
    $\left( {\frac{4}{5},\frac{{12}}{5}} \right)$
  • B
    $\left( {\frac{3}{5},\frac{{23}}{{10}}} \right)$
  • C
    $\left( {\frac{11}{20},\frac{{29}}{{10}}} \right)$
  • D
    $\left( {\frac{3}{10},\frac{{17}}{{5}}} \right)$
✓

Answer

Correct option: A.
$\left( {\frac{4}{5},\frac{{12}}{5}} \right)$
a
Equation of line $L$

$\frac{x}{2} + \frac{y}{4} = 1$

$2x + y = 4\,\,\,\,\,\,\,\,\,\,.....\left( 1 \right)$

For line 

$x - 2y =  - 4\,\,\,\,\,.......\left( 2 \right)$

solving equation  $(1)$ and $(2)$; we get point of intersection

$\left( {4/5,\frac{{12}}{5}} \right)$

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