Question
Translate triangle ABC by 3 units to the left and 5 units down. Which of the following are the coordinates of new triangle A'B'C"?
(1 point)
O A'(-1, 2), B'(-3, -2), C'(2, 0)
O A'(1, 0), B'(-1, -4), C'(4, - 2)
O A'(1,10), B'(-1, 6), C' (4, 7)
O A' (7, 0), B'(5, - 4), C' (10, -2)
(1 point)
O A'(-1, 2), B'(-3, -2), C'(2, 0)
O A'(1, 0), B'(-1, -4), C'(4, - 2)
O A'(1,10), B'(-1, 6), C' (4, 7)
O A' (7, 0), B'(5, - 4), C' (10, -2)
Answers
GPT-4o mini
To translate triangle ABC by 3 units to the left and 5 units down, you need to subtract 3 from the x-coordinates and 5 from the y-coordinates of each vertex of the triangle.
Let the original coordinates of points A, B, and C be given as \( A(x_1, y_1), B(x_2, y_2), C(x_3, y_3) \).
After translation, the new coordinates will be:
- A' = \( (x_1 - 3, y_1 - 5) \)
- B' = \( (x_2 - 3, y_2 - 5) \)
- C' = \( (x_3 - 3, y_3 - 5) \)
Since we do not have the original coordinates of triangle ABC, we will instead check which of the following options correspond to the translation described above.
Let's look at each option to see if it corresponds to a translation of 3 units left and 5 units down from any point:
1. **Option A:** A'(-1, 2), B'(-3, -2), C'(2, 0)
- A' : \( (-1 + 3, 2 + 5) = (2, 7) \)
- B' : \( (-3 + 3, -2 + 5) = (0, 3) \)
- C' : \( (2 + 3, 0 + 5) = (5, 5) \)
- Not a valid original position.
2. **Option B:** A'(1, 0), B'(-1, -4), C'(4, -2)
- A' : \( (1 + 3, 0 + 5) = (4, 5) \)
- B' : \( (-1 + 3, -4 + 5) = (2, 1) \)
- C' : \( (4 + 3, -2 + 5) = (7, 3) \)
- Not a valid original position.
3. **Option C:** A'(1, 10), B'(-1, 6), C'(4, 7)
- A' : \( (1 + 3, 10 + 5) = (4, 15) \)
- B' : \( (-1 + 3, 6 + 5) = (2, 11) \)
- C' : \( (4 + 3, 7 + 5) = (7, 12) \)
- Not a valid original position.
4. **Option D:** A'(7, 0), B'(5, -4), C'(10, -2)
- A' : \( (7 + 3, 0 + 5) = (10, 5) \)
- B' : \( (5 + 3, -4 + 5) = (8, 1) \)
- C' : \( (10 + 3, -2 + 5) = (13, 3) \)
- Not a valid original position.
None of the options provided directly represent a valid triangle after translating 3 units to the left and 5 units down based on any original points. This might mean that either the original coordinates were not included or the options given do not correspond to any valid translations based on the described movement.
If you know the original coordinates, you can apply this method to find the translated coordinates correctly. If you want me to help you analyze something else, please let me know!
Let the original coordinates of points A, B, and C be given as \( A(x_1, y_1), B(x_2, y_2), C(x_3, y_3) \).
After translation, the new coordinates will be:
- A' = \( (x_1 - 3, y_1 - 5) \)
- B' = \( (x_2 - 3, y_2 - 5) \)
- C' = \( (x_3 - 3, y_3 - 5) \)
Since we do not have the original coordinates of triangle ABC, we will instead check which of the following options correspond to the translation described above.
Let's look at each option to see if it corresponds to a translation of 3 units left and 5 units down from any point:
1. **Option A:** A'(-1, 2), B'(-3, -2), C'(2, 0)
- A' : \( (-1 + 3, 2 + 5) = (2, 7) \)
- B' : \( (-3 + 3, -2 + 5) = (0, 3) \)
- C' : \( (2 + 3, 0 + 5) = (5, 5) \)
- Not a valid original position.
2. **Option B:** A'(1, 0), B'(-1, -4), C'(4, -2)
- A' : \( (1 + 3, 0 + 5) = (4, 5) \)
- B' : \( (-1 + 3, -4 + 5) = (2, 1) \)
- C' : \( (4 + 3, -2 + 5) = (7, 3) \)
- Not a valid original position.
3. **Option C:** A'(1, 10), B'(-1, 6), C'(4, 7)
- A' : \( (1 + 3, 10 + 5) = (4, 15) \)
- B' : \( (-1 + 3, 6 + 5) = (2, 11) \)
- C' : \( (4 + 3, 7 + 5) = (7, 12) \)
- Not a valid original position.
4. **Option D:** A'(7, 0), B'(5, -4), C'(10, -2)
- A' : \( (7 + 3, 0 + 5) = (10, 5) \)
- B' : \( (5 + 3, -4 + 5) = (8, 1) \)
- C' : \( (10 + 3, -2 + 5) = (13, 3) \)
- Not a valid original position.
None of the options provided directly represent a valid triangle after translating 3 units to the left and 5 units down based on any original points. This might mean that either the original coordinates were not included or the options given do not correspond to any valid translations based on the described movement.
If you know the original coordinates, you can apply this method to find the translated coordinates correctly. If you want me to help you analyze something else, please let me know!