Question

what are three ways to denote a translation?

Answer 1

@mathmate

Answer 2

Start with the point A (3, 1). Translate the point 1 unit to the left and 4 units down. What are the new coordinates of the point A’? Now translate A’ 3 unit to the left and 2 units up. What are the new coordinates of the point A’’? What translation would need to be made in order for the result to be the original point A (3, 1)?
how about this one?

Answer 3

For the second question, if we denote
t: (x,y) -> (x+h, y+k)
by the operator T(h,k), then
A'=T(-1,-4)A
and
A"=T(-2,+2)A'
So
A"=T(-1,-4) T(-2,+2) A
=T(-3,-2)A

To go from A" to A, take the inverse transformation, which is the negative of T(-3,-2), or T(3,2).

Answer 4

thank you!!