The point P has coordinates (rcosφ, rsinφ) where the distance of P from the origin
is OP=r and the line OP is at angle φ to
the x axis. Find the image of this point under
the transformation given by the matrix
T1 =
cos θ
−sinθ
sin θ
cos θ
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 = xtanθ. 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 ' = pcos2θ. Find the lengths
BP ' , AX ' and BX ' and hence prove that
transformation given by the matrix
The point P has coordinates (rcosφ, rsinφ) where the distance of P from the origin
is OP=r and the line OP is at angle φ to
the x axis. Find the image of this point under
the transformation given by the matrix