Redu Congruence and Rigid Transformations
Rectangle ABCD is congruent to rectangle A"B"C"D"
A А
Which sequence of transformations could have been used to
transform rectangle ABCD to produce
rectangle A"B"C"D" ?
B
12
Rectangle ABCD was rotated 180° around the
origin and then translated 7 units down
A
B
O
Rectangle ABCD was translated 8 units left and
then 7 units down
Rectangle ABCD was reflected across the y-axis
and then across the x-axis
AK12
H
hD

a negative exponent is translated as follows:

so, we have

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."

shorter then the tree