write the following composition as one translation: T3,5 0 T4,-4
To translate the composition T3,5 0 T4,-4, follow these steps:
1. Start at the point (3, 5)
2. Translate (move) 0 units horizontally and 4 units downwards. This results in the new point (3, 1).
To translate the composition T3,5 0 T4,-4, we first perform a translation of (3 units to the right, 5 units up) using the notation T(a, b). Then, we perform a second translation of (4 units to the right, 4 units down) denoted by T(c, d).
To combine these two translations into one translation, we add the x-components and y-components separately.
For the x-component, we add 3 and 4 together, which gives us a total of 7 units to the right.
For the y-component, we add 5 and -4, which gives us a total of 1 unit up.
Therefore, the translation T3,5 0 T4,-4 can be written as a single translation T7,1.