The composition of translations T(-3, 4) ∘ T(8, -7)(x, y) is equivalent to a single translation T(5, -3)(x, y), moving the point 5 units to the right and 3 units down.
The composition of translations T(-3, 4) ∘ T(8, -7)(x, y) represents a sequence of two translations applied to a point (x, y). Each translation is denoted by a vector, where the first translation T(-3, 4) moves the point left by 3 units and up by 4 units, and the second translation T(8, -7) moves the point right by 8 units and down by 7 units.
To find the overall effect as a single translation, we can sum the vector components of the translations:
The combined horizontal (x) translation is: -3 + 8 = 5.
The combined vertical (y) translation is: 4 + (-7) = -3.
Therefore, the composition of translations T(-3, 4) ∘ T(8, -7)(x, y) is equivalent to a single translation T(5, -3)(x, y).
This means that the point (x, y) undergoes a net translation of 5 units to the right and 3 units down.
The question probable may be:
What is the composition of the translations
(T〈−3, 4〉 ∘ T〈8, −7〉)(x, y) as one translation?