Statement-1 : The point A (1,0,7) is the mirror image of the point B (1,6,3) in the line \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}

Statement-2 : The line : \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} bisects  the line segment joining A (1,0,7) and B (1,6,3).

 

  • Option 1)

    Statement-1 is true, Statement-2 is false.

  • Option 2)

    Statement-1 is false, Statement-2 is true.

  • Option 3)

    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

  • Option 4)

    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

 

Answers (1)

As we learnt in 

Image of a point -

Let L' be the image of point P\left ( \alpha ,\beta ,\gamma \right ) in the plane ax+by+cz+d=0

L' will be given by the formula 

\frac{x-\alpha }{a}=\frac{y-\beta }{b}=\frac{z-\gamma }{c}= \frac{-2\left ( a\alpha +b\beta +c\gamma +d \right )}{a^{2}+b^{2}+c^{2}}

-

 

 Image of B(1,6,3)is A(1,0,7)

But it is not necessary that a plane will always bisect the line AB. So,it is not the correct explanation of statement 1.

 


Option 1)

Statement-1 is true, Statement-2 is false.

Incorrect option

Option 2)

Statement-1 is false, Statement-2 is true.

Incorrect option

Option 3)

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Incorrect option

Option 4)

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

Correct option

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