Question

What is the composition of the translations (T2-3,4> T8, -7>) (x, y) as one translation?(T<-3,4> T8, -7>)(x, y) = Tsp,(x, y) where p =and q =

Answer 1

We have two translations and we have to find a translation that is equivalent.

When the transformations are translations, the equivalent transformation is the net effect in eah of the coordinates and can be calculated as the sum of each translation.

For example, in the x-coodinates, the first transformation is:

`x\longrightarrow x-3`

And the second, applied to the result, is:

`x-3\longrightarrow(x-3)+8=x+5`

The net effect is a translation of five units to the right, what could have been calculated as -3+8=5.

If we do the same for the y-coordinates, the net effect is 4-7=-3.

So we can write the net translation as:

`(T<-3,4>\circ T<8,-7>)(x,y)=T<5,-3>(x,y)`

Answer:

Equivalent translation: T<5,-3>

p=5

q=-3