Question

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 $(\frac{-22}{7},\frac{-3}{14},\frac{-13}{14})$

• A. $\frac{-58}{7},\frac{36}{14},\frac{-40}{14}$
• B. $\frac{-44}{7},\frac{-6}{14},\frac{-26}{14}$
• C. $\frac{44}{7},\frac{6}{14},\frac{-30}{14}$
• D. $\frac{-44}{7},\frac{6}{14},\frac{-30}{14}$

Answer 1

The correct option is A

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

We know that midpoint of P and I (image) is foot of the perpendicular Q. We can find the coordinates of I if we know the coordinates of P and Q. We are given these two in question Let the coordinates of I be (x,y,z). $MidpointofPandI=(\frac{x+2}{2},\frac{y-3}{2},\frac{z+1}{2})=Q=(\frac{-22}{7},\frac{-3}{14},\frac{-13}{14})\Rightarrow \frac{x+2}{2}=\frac{-22}{7},\frac{y-3}{2}=\frac{-3}{14},\frac{z+1}{2}=\frac{-13}{14}\Rightarrow x=\frac{-58}{7},y=\frac{36}{14},z=\frac{-40}{14}SothecoordinatesofimageIare(\frac{-58}{7},\frac{36}{14},\frac{-40}{14})$