What translation rule can be used to describe the result of the composition of (x, y) (x – 9, y – 2) and (x, y) (x + 1, y – 2)
are you saying,
(x,y) ---> (x-9,y-2) is followed by (x,y)-->(x+1,y-2) ?
then (x,y) ---> (x-8, y-4)
Reiny is correct.
To find the composition of two translations, you need to consider the effect of applying one translation followed by the other.
Let's denote T₁: (x, y) ⟼ (x - 9, y - 2) as the first translation, and T₂: (x, y) ⟼ (x + 1, y - 2) as the second translation.
To determine the result of the composition, we apply T₁ first and then T₂.
When we apply T₁: (x, y) ⟼ (x - 9, y - 2), the point (x, y) is translated 9 units left and 2 units down.
Next, we apply T₂: (x, y) ⟼ (x + 1, y - 2). This translation moves the point further by 1 unit to the right and 2 units down.
Therefore, the composition of T₁ and T₂ is equivalent to the translation (x, y) ⟼ (x - 9 + 1, y - 2 - 2), which simplifies to (x, y) ⟼ (x - 8, y - 4).
So, the translation rule that describes the result of the composition (x, y) ⟼ (x - 9, y - 2) and (x, y) ⟼ (x + 1, y - 2) is (x, y) ⟼ (x - 8, y - 4).
To find the translation rule that describes the composition of two translation vectors, we need to perform the composition operation, which involves applying one vector followed by the other.
Let's start with the first vector: (x, y) -> (x - 9, y - 2).
This means that for any given point (x, y), we translate it by moving 9 units to the left (subtracting 9 from the x-coordinate) and 2 units down (subtracting 2 from the y-coordinate).
Next, we apply the second vector: (x, y) -> (x + 1, y - 2).
This means that for any given point (x, y), we translate it by moving 1 unit to the right (adding 1 to the x-coordinate) and 2 units down (subtracting 2 from the y-coordinate).
To perform the composition, we need to apply the second vector to the result of the first vector.
Let's substitute the first vector into the second vector:
(x - 9, y - 2) -> (x - 9 + 1, (y - 2) - 2) = (x - 8, y - 4).
Therefore, the translation rule that describes the composition of the given translation vectors is:
(x, y) -> (x - 8, y - 4).
This means that for any given point (x, y), we translate it by moving 8 units to the left (subtracting 8 from the x-coordinate) and 4 units down (subtracting 4 from the y-coordinate).