Question

Find the image of:
(i) point $(5,2,-7)$ in XY-plane
(ii) point $(-4,0,7)$ in XZ-plane

Answer 1

The fig(i) shows three directions along x-axis,y-axis,z-axis.

$P(5,2,-7)$ be the point & $I$ be its image and $F$ be its foot $\perp$ in x-y plane $\Rightarrow z=0$

$\therefore F=(5,2,0)$

$PF=FI$ (image is equidistant from mirror as object is from mirror)

$\therefore F$ divides $PI$ in $1:1$.

$\therefore I=(5,2,7)$.

The fig(ii) shows three directions along x-axis,y-axis,z-axis.

$P(-4,0,7)$ be the point & $I$ be its image.

and $F$ be its foot of $\perp$ in x-z plane $\Rightarrow y=0$

$\therefore F=(-4,0,7)$

$PF=FI\Rightarrow F$divides $PI$ in $1:1$.

$\therefore I=(-4,0,7)$