Describe a sequence of transformations that maps A' B' C' D' onto ABCD.
[it wont allow me to put a picture so ill put the points]
A'(-4,2) B'(-2,2) C'(-4,3) D'(-2,3)
A(2,-2) B(4,-2) C(4,-3) D(2,-3)
I need an answer by the end of tonight!!!!
To map A'(-4,2) B'(-2,2) C'(-4,3) D'(-2,3) onto ABCD, we can follow the steps below:
1. Translation: Move all the points 6 units to the right and 4 units down.
- A'(-4,2) becomes A'(-4+6, 2-4) = A'(2,-2)
- B'(-2,2) becomes B'(-2+6, 2-4) = B'(4,-2)
- C'(-4,3) becomes C'(-4+6, 3-4) = C'(2,-3)
- D'(-2,3) becomes D'(-2+6, 3-4) = D'(4,-3)
2. Reflection: Reflect all the points about the y-axis.
- A'(2,-2) becomes A'(-2,-2)
- B'(4,-2) becomes B'(-4,-2)
- C'(2,-3) becomes C'(-2,-3)
- D'(4,-3) becomes D'(-4,-3)
Therefore, the sequence of transformations that maps A' B' C' D' onto ABCD is a translation 6 units to the right and 4 units down, followed by a reflection about the y-axis.
To describe a sequence of transformations that maps A' B' C' D' onto ABCD, we can use a combination of translation and reflection.
1. Translation:
- We need to shift the points A' B' C' D' to match the coordinates of A B C D along the x-axis by adding 6 to all x-coordinates.
- The translation vector is (6, 0).
2. Reflection:
- We need to reflect the translated points across the y-axis to match the coordinates of A B C D.
- The reflection can be achieved by changing the sign of the x-coordinates.
Applying these transformations to A' B' C' D', we get:
A'' = (A' + translation) after reflection
B'' = (B' + translation) after reflection
C'' = (C' + translation) after reflection
D'' = (D' + translation) after reflection
Let's calculate the new coordinates:
A'' = (-4, 2) + (6, 0) after reflection
= (-4 + 6, 2)
= (2, 2)
B'' = (-2, 2) + (6, 0) after reflection
= (-2 + 6, 2)
= (4, 2)
C'' = (-4, 3) + (6, 0) after reflection
= (-4 + 6, 3)
= (2, 3)
D'' = (-2, 3) + (6, 0) after reflection
= (-2 + 6, 3)
= (4, 3)
Hence, the sequence of transformations that maps A' B' C' D' onto ABCD is a translation followed by a reflection:
- Translate (6, 0)
- Reflect across the y-axis.