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)?
I am stuck can you please explain
Rotations quiz
1. C , MN
2. C , left corner
3. B , ( x - 6, y - 6); ( -11 , -5)
4. A 7 units left and 7 units down
5. D , (x + 3 , y - 5)
6. C, ( x - 8, y - 4)
7. C, P'(-4 , -7) Q' (-8, -7) R' (-3 , 3)
8. C , (4, -9)
9. D , OF
10. A , 72 degrees
The first rule sends (x, y) to (x - 9, y - 2). That is, it slides every point to the left nine units and down two units.
The second rule slides every point to the right 1 unit and down 2 units.
The composition is combining the two transformations. In this case, they are both translations (slides), so it doesn't really matter which order you do them in.
The first translation could be written in vector form as <-9, -2> and the second is <+1, -2>. To figure out the combined effect, just add the components.
<-9 + (+1), -2 + (-2)>
<-8, -4>
So a single slide left 8 and down 4 does the same thing as the two rules combined.
(x, y) --> (x - 8, y - 4)
would be a translation rule to use.
Note: Sometimes the order you do transformations matters. For example, translate then reflect might be different from reflect, then translate. But in the case of two translations, it doesn't really matter which order you do the slides. You could have done rule 2 first, then rule 1 second.
That's because
(x - 9 - 2, y - 2 + 1) is the same as
(x - 2 - 9, y + 1 - 2).
@willie i dont have that as a option on my quiz
It's c
Hasan Piker is 100% correct however i got a 80% because i read it wrong the first time xd
Hasan Piker is 100%!
Willie literally tells you the answer if you just read through it
Hasannn is riiighttt
To find the translation rule that describes the result of the composition of the two given translations, we need to understand what each translation does to the original coordinates.
Let's break down each translation:
1. (x, y) → (x – 9, y – 2):
This translation subtracts 9 from the x-coordinate and subtracts 2 from the y-coordinate. In other words, it shifts the point 9 units to the left (in the x-direction) and 2 units downward (in the y-direction).
2. (x, y) → (x + 1, y – 2):
This translation adds 1 to the x-coordinate and subtracts 2 from the y-coordinate. It shifts the point 1 unit to the right (in the x-direction) and 2 units downward (in the y-direction).
Now, to compose these two translations, we apply the second translation first and then apply the first translation to the result.
Let's denote the composition of the two translations as T(x, y).
First, we apply (x, y) → (x + 1, y – 2):
The x-coordinate becomes (x + 1) and the y-coordinate becomes (y – 2). So, the intermediate result is (x + 1, y – 2).
Next, we apply (x + 1, y – 2) → (x – 9, y – 2):
The x-coordinate becomes (x + 1 – 9) = (x – 8) and the y-coordinate remains the same (y – 2). So, the final result is (x – 8, y – 2).
Therefore, the translation rule that describes the result of the composition is:
T(x, y) = (x – 8, y – 2).
This rule tells us that the composition of the two given translations will shift any point 8 units to the left (in the x-direction) and 2 units downward (in the y-direction).