Question

What is the composition of the translations (T ∘ T ) (x, y) written as one translation? (T ∘ T )(x, y) = T (x, y) where m =___and n = ___

Answer 1

The composition of the translation T with itself creates a new translation that doubles the movement in both the x and y directions, resulting in m = 2m and n = 2n for the composed translation.

Step-by-step explanation:

The student is asking about composing two translations in a plane in Mathematics. A translation T in math is a function that moves every point a certain distance in a given direction. If you have T(x, y) which translates a point (x, y) by certain amounts m and n in the x and y directions respectively, the composition of that translation with itself (T ∘ T) would be a translation that moves every point by 2m in the x direction and 2n in the y direction.

Thus, if T(x, y) represents a translation by m in the x direction and n in the y direction, then (T ∘ T)(x, y) = T(T(x, y)) translates the point by 2m in the x direction and 2n in the y direction, giving us m = 2m and n = 2n.