This document provides the steps to find the image of point (1,2,-1) in the plane 2x + y - z = 2. It shows that the direction ratios of the line perpendicular to the plane are equal to the normal of the plane. It then finds the equation of the line through the point (1,2,-1) perpendicular to the plane. By setting up and solving two equations, it determines that the image point is (0,3,-1).

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Finding image of a point through a plane.
S
Q. Find the image of point (1,2,-1) in the plane 2x + y – z = 2.
Any line perpendicular to a plane will have DR same as normal to plane.
Therefore DR of a line perpendicular to given plane
The equation of line through (1,2,-1) & ⊥
−
∴
=
− )
()
−
=
+
−
=
(
∴ (
I
, ,−
T
I
=
+ ,
J
+ ,−
+ ) + ( + ) − (—
− )=
E
−
×
H
−
+ ,
−
+ ,
−(− )
()
D
U
−
C
&
, ,
A (1,2,-1)
Let image be point P
T
Point B is midpoint of A & P
∴
=
+
,
=
+
A
B(0, 3/2, -1/2)
,
−
=
−
I
O
N
(− , , )
Image point P(x1,y1,z1)