The point P has coordinates (rcosf, rsin f) where the distance of P from the origin
is OP=r and the line OP is at angle f to
the x axis. Find the image of this point under
the transformation given by the matrix
T1 =
æ ç
è
cos q
-sinq
sin q
cos q
ö ÷
ø
Draw a diagram and
describe the effect of this transformation on the
points of the plane.
The point P has coordinates (p,q) and the
point P¢ is the reflection of P in the line
y = xtanq. In the diagram below the lines
P¢X¢ and XA¢ are perpendicular to the line
OA¢X¢.
"
Prove that OX = OX¢ = p, P¢X¢ = PX = q and
OA = OA¢ = pcos2q. Find the lengths
BP¢, AX¢ and BX¢ and hence prove that
transformation given by the matrix
