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 L1 is the line perpendicular to L and passing through the point (-2, 1), then the point of intersection of L and L1 is :

  • Option 1)

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

  • Option 2)

    \left ( \frac{11}{20} ,\frac{29}{10}\right )

  • Option 3)

    \left ( \frac{3}{10} ,\frac{17}{5}\right )

  • Option 4)

    \left ( \frac{3}{5} ,\frac{23}{10}\right )

 

Answers (2)

As we learnt in 

Intercept form of a straight line -

\frac{x}{a}+\frac{y}{b}=1

 

- wherein

a and b are the x-intercept and y -intercept respectively.

 

Equation of a line perpendicular to a given line -

Bx-Ay+\lambda =0  is the line perpendicular to Ax+By+C =0 .

 

- wherein

  \lambda is some other constant  than C.

 

 Here a=2, b=4

hence equation of straight line is \frac{x}{2}+\frac{y}{4}=1 (intercept form)

L:2x+y=4

Line \perp to L is x-2y+\lambda =0

Passing through (-2, 1)

-2-2+\lambda =0\Rightarrow \lambda =4

x-2y+4=0

\left 2x+y-4=0 \right ]\times 2

4x+2y-8=0

\underline{x-2y+4=0}

x=\frac{4}{5}, y=\frac{12}{5}


Option 1)

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

Correct option

Option 2)

\left ( \frac{11}{20} ,\frac{29}{10}\right )

Incorrect Option

Option 3)

\left ( \frac{3}{10} ,\frac{17}{5}\right )

Incorrect Option

Option 4)

\left ( \frac{3}{5} ,\frac{23}{10}\right )

Incorrect Option

Option no. 1

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