TRANSFORMATION IN THE PLANE
Transformation in the plane is a mapping which shifts an object from one position to another within the same plane.
Examples of transformations in the xy plane are
i. Reflection
ii. Rotation
iii. Enlargement
iv. Translation
REFLECTION
-The action or process of sending back light, heat or sound from a surface.
ISOMETRIC MAPPING
-Is a transformation which the object size is maintained.
-Reflection is an example of isometric mapping.
Reflection in the line included an angle (α) passing through the origin.
inclined at B with the coordinates being (X, Y) is the image of under reflection is 
PP is perpendicular to OS (
is the line of reflection)POS= α
βΔ OPQ is right angled a
t Q
Hence X = OP cos B……(i)
Y = OP sin B
is perpendicular to the axis of X at RCoordinates of R are ( X1,0)
OR= X 1
RP1=Y1
Δ OP1R is right angled at R
P1OS= POS= α-β
Angle P1OR = α – β + α – β + β = 2α – β
Cos (2α-β)= X1
OP1
X1= OP1cos (2α-β)….. (iii)
Y1 = sin (2α-β)
OP1
Y1=OP1sin (2α-β)……(iv)
Cos (A+B) = cos A cos B – sin A sin B
Sin(A+B) = sin A cos B+ sin B cos A
X1 = OP1 cos 2α cosβ + OP sin 2α cos β…. (iii)
Y1= OP sin 2α cos β – OP1 sin B cos 2α
X1= OP cos 2α cos β+ OP sin 2α sin β
Y1= OPsin2αcos β – Op sinβ cos 2α
X1 = OP cos β cos2α + OP sin β sin 2α
Y1= OP cos βsin 2α – OP sin β cos 2α
X1 = X cos 2α + Y sin 2α …..( i)
Y1 = X sin 2α – Y cos 2 α …..(ii)
= 
Exercise
1. Find the image of the point A (1, 2) after a reflection in the Y= X plane.
Solution;
Y= X
= 1Tan α =
= 1α= 900
= 
= 
