Invariance Flashcards
1
Q
invariant point is
A
point which is mapped to itself by the
transformation.
2
Q
how to find invariant points part 1
A
(a c) (x) = (x)
b d) (y) (y
3
Q
how to find invariant points part 2
A
ax + cy = x
bx + dy = y
4
Q
how to find invariant points part 3
A
if equations are equivalent to each other, LINE OF INVARIANT POINTS + all points on the line can be represented in terms of a parameter.
if not = ONLY INV POINT IS ORIGIN
5
Q
invariant line is
A
line which is mapped to itself by the transformation
6
Q
line of invariant points is an invariant line, but
A
an invariant line is not necessarily a line of invariant points!
7
Q
how to find invariant line
A
M( x ) = x’
(mx +c) y’
image point must lie on the line y = mx + c
y’ = m(x’) + c
rearrange and factorise to get m
