QJEEM11Ma4743: JEE Main 2011 Mathematics - Class 12 JEEM11Ma4743 Solution: Statement - 1 : The point A ( 1 , 0 , 7 ) is the mirror image…

Question

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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)

A Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
B Statement -1 is true, Statement - 2 is false.
C Statement - 1 is false , Statement -2 is true.
D Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement -1.

Accepted Answer

The directions ratios of the line segment joining points

A (1, 0, 7)

and

B (1, 6, 3)

are

0, 6, - 4.

The direction ratios of the given line are

1, 2, 3.

Clearly

1 \times 0 + 2 \times 6 + 3 \times (- 4) = 0

So, the given line is perpendicular to line

A B .

Also, the mid point of

A

and

B

is

(1, 3, 5)

which lies on the given line.

So, the image of

B

in the given line is

A

, because the given line is the perpendicular bisector of line segment joining points

A

and

B

, But statement -

2

is not a correct explanation for statement

- 1.

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