Image of a Point with Respect to a Line

Q. The reflection of the point P(1, 0, 0) in the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{x+10}{8}$ is

1. (5, - 8, - 4)
2. (1, - 1, - 10)
3. (2, - 3, - 8)
4. (3, -4, -2)

Q. Let $a,b\in R.$ If the mirror image of the point $P(a,6,9)$ with respect to the line $\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}$ is $(20,b,-a-9),$ then $|a+b|$ is equal to

1. $86$
2. $88$
3. $84$
4. $90$

Q.

Find the image of the point (1, 6, 3) with respect to the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is ___.

1. $(1,3,5)$

2. $(1,-6,11)$
3. $(1,0,7)$
4. $(1,2,3)$

Q. Find the mirror image of the point $(1,2,2)$ on the line
$\frac{x-5}{2}=\frac{y-3}{2}=\frac{z-2}{1}$ .

1. $\left(\frac{23}{9},-\frac{40}{9},-\frac{38}{9}\right)$
2. $\left(\frac{41}{9},\; -\frac{4}{9},\; -\frac{2}{9}\right)$
3. $(23,40,38)$
4. $(23,-40,-38)$

Q. The image of $x+y+z+1=0$, through the plane $2x–4y+2z+4=0,$ is

1. $2x+2y+2z+{\lambda }_1=0$
2. $x+y+z+1=0$
3. $x+y+z+\lambda =0$
4. $x+y+z+4=0$

Q.

Find the image of the point (1, 6, 3) with respect to the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is ___.

1. $(1,3,5)$

2. $(1,-6,11)$
3. $(1,0,7)$
4. $(1,2,3)$

Q.

Find the image of the point $P(2,-3,1)$ about the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z+2}{-1}$

1. $(\frac{-58}{7},\frac{36}{14},\frac{-40}{14})$

2. $(\frac{58}{7},\frac{36}{14},\frac{-40}{14})$

3. $(\frac{-58}{7},\frac{36}{14},\frac{40}{14})$

4. $(1,-3,2)$

Q.

Image of a point P(2, -3, 1 ) with respect to line L is I. Find the coordinates of I, if foot of the perpendicular of P with respect to L is $(\frac{-22}{7},\frac{-3}{14},\frac{-13}{14})$

1. 

2. 

3. 

4. 

Q.

Find the position vector of the mid-point of the vector joining points P(2, 3, 4) and Q(4, 1, -2).

Q.

Find the image of the point (1, 6, 3) with respect to the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is ___.

1. $(1,0,7)$

2. $(1,3,5)$

3. $(1,2,3)$
4. $(1,-6,11)$

Q. If the line $4x+3y+1=0$ meets the parabola $y^2=8x$ then mid point of the chord is

1. (-1, 1)
2. (2, -3)
3. (3, -3)
4. (5, -7)

Q. The reflection of the point P(1, 0, 0) in the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{x+10}{8}$ is

1. (3, -4, -2)
2. (5, - 8, - 4)
3. (1, - 1, - 10)
4. (2, - 3, - 8)

Q. The image of the point $(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ is

1. $(1,0,7)$
2. $(1,3,5)$
3. $(-1,-6,-3)$
4. $(2,4,6)$

Q.

Find the image of the point $P(2,-3,1)$ about the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z+2}{-1}$

1. $(1,-3,2)$

2. $(\frac{-58}{7},\frac{36}{14},\frac{-40}{14})$

3. $(\frac{58}{7},\frac{36}{14},\frac{-40}{14})$

4. $(\frac{-58}{7},\frac{36}{14},\frac{40}{14})$

Q.

Find the image of the point $P(2,-3,1)$ about the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z+2}{-1}$

1. $(1,-3,2)$

2. $(\frac{-58}{7},\frac{36}{14},\frac{-40}{14})$

3. $(\frac{58}{7},\frac{36}{14},\frac{-40}{14})$

4. $(\frac{-58}{7},\frac{36}{14},\frac{40}{14})$

Q.

Find the image of the point $P(2,-3,1)$ about the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z+2}{-1}$

1. $(1,-3,2)$

2. $(\frac{-58}{7},\frac{36}{14},\frac{-40}{14})$

3. $(\frac{58}{7},\frac{36}{14},\frac{-40}{14})$

4. $(\frac{-58}{7},\frac{36}{14},\frac{40}{14})$

Q.

Image of a point P(2, -3, 1 ) with respect to line L is I. Find the coordinates of I, if foot of the perpendicular of P with respect to L is $(\frac{-22}{7},\frac{-3}{14},\frac{-13}{14})$

1. 

2. 

3. 

4. 

Q. The reflection of the point P(1, 0, 0) in the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{x+10}{8}$ is

1. (1, - 1, - 10)
2. (2, - 3, - 8)
3. (3, -4, -2)
4. (5, - 8, - 4)

Q.

Image of a point P(2, -3, 1 ) with respect to line L is I. Find the coordinates of I, if foot of the perpendicular of P with respect to L is $(\frac{-22}{7},\frac{-3}{14},\frac{-13}{14})$

1. $\frac{-58}{7},\frac{36}{14},\frac{-40}{14}$

2. $\frac{-44}{7},\frac{-6}{14},\frac{-26}{14}$

3. $\frac{44}{7},\frac{6}{14},\frac{-30}{14}$

4. $\frac{-44}{7},\frac{6}{14},\frac{-30}{14}$

Q. The reflection of the point P(1, 0, 0) in the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{x+10}{8}$ is

1. (3, -4, -2)
2. (5, - 8, - 4)
3. (1, - 1, - 10)
4. (2, - 3, - 8)

Q. Find the mirror image of the point $(1,2,2)$ on the line
$\frac{x-5}{2}=\frac{y-3}{2}=\frac{z-2}{1}$ .

1. $(23,40,38)$
2. $(23,-40,-38)$
3. $\left(\frac{23}{9},-\frac{40}{9},-\frac{38}{9}\right)$
4. $\left(\frac{41}{9},\; -\frac{4}{9},\; -\frac{2}{9}\right)$

Q. Find the mirror image of the point $(1,2,2)$ on the line
$\frac{x-5}{2}=\frac{y-3}{2}=\frac{z-2}{1}$ .

1. $(23,40,38)$
2. $(23,-40,-38)$
3. $\left(\frac{23}{9},-\frac{40}{9},-\frac{38}{9}\right)$
4. $\left(\frac{41}{9},\; -\frac{4}{9},\; -\frac{2}{9}\right)$