Given quadrilateral ABCD (preimage),
perform various transformations to find the coordinates for it's
image, quadrilateral A'B'C'D'.
In the "Algebra Window," double-click
on "u" and "v" to change the values of the
transformation matrix.
For a reflection over the
x-axis,
multiply the vertex matrix on the left by:
\left| \matrix{ 1 & 0 \cr 0
& -1} \right|
For a reflection over the
y-axis,
multiply the vertex matrix on the left by:
\left| \matrix{ -1 & 0 \cr
0 & 1} \right|
For a reflection over the
line \quad y = x,
multiply the vertex matrix on the left by:
\left| \matrix{ 0 & 1 \cr 1
& 0} \right|
For a counterclockwise rotation
of
90°,
multiply the vertex matrix on the left by:
\left| \matrix{ 0 & -1 \cr
1 & 0} \right|
For a counterclockwise rotation
of
180°,
multiply the vertex matrix on the left by:
\left| \matrix{ -1& 0 \cr 0
& -1} \right|
For a counterclockwise rotation
of
270°,
multiply the vertex matrix on the left by:
\left| \matrix{ 0 & 1 \cr -1
& 0} \right|
