Question
Translate triangle ABC by 3 units to the left and 5 units down. Which of the following are the coordinates of the new triangle A’ B’ C’?
A’ (1,0), B’ (-1,-4), C’ (4,-2)
A’(7,0), B’(5,-4), C’(10,-2)
A’(-1,2), B’(-3,-2), C’(2,0)
A’(1,10), B’(-1,6), C’(4,7)
A’ (1,0), B’ (-1,-4), C’ (4,-2)
A’(7,0), B’(5,-4), C’(10,-2)
A’(-1,2), B’(-3,-2), C’(2,0)
A’(1,10), B’(-1,6), C’(4,7)
Answers
GPT-4o mini
To determine the coordinates of triangle A'B'C' after translating triangle ABC by 3 units to the left and 5 units down, we first need to understand the translation operation.
When we translate a point \( (x, y) \):
- Moving 3 units to the left means we subtract 3 from the x-coordinate: \( x' = x - 3 \)
- Moving 5 units down means we subtract 5 from the y-coordinate: \( y' = y - 5 \)
Therefore, the new coordinates \( (x', y') \) will be calculated as:
\[ x' = x - 3 \]
\[ y' = y - 5 \]
Now, since we don't have the original coordinates of points A, B, and C, we cannot compute the new coordinates directly. However, we can check which of the provided answer choices could realistically result from such a translation.
Let's examine the provided answer choices for signs:
- The process of translating points typically increases negative coordinates (as they move "down" in value) and further reduces positive ones.
Checking the answer choices with this observation:
1. **A’(1,0), B’(-1,-4), C’(4,-2)** - Here you have varying changes, but generally, they are mixed and unclear.
2. **A’(7,0), B’(5,-4), C’(10,-2)** - These are all positives and would imply an upward movement, contradicting our downward movement.
3. **A’(-1,2), B’(-3,-2), C’(2,0)** - This choice shows negatives and a positive (+2), but it's still potentially valid.
4. **A’(1,10), B’(-1,6), C’(4,7)** - All points are shifted positively, which also contradicts the downward movement.
For a valid translate, we'd expect outputs with consistently minimized coordinates suggesting downward translation should appear negative or reduced significantly in Y-planar movements.
Let's summarize:
- The new coordinates arising from a left side (negative X) and downward (negative Y) shift should indeed reflect negative movements.
Out of the choices examined, **A'(-1,2), B'(-3,-2), C'(2,0)** looks potentially valid as the only choice that holds some required downward elements, while the others don't fit logically with expected outputs post-translation at all.
Thus, **the best candidate is: A’(-1, 2), B’(-3, -2), C’(2, 0)**.
When we translate a point \( (x, y) \):
- Moving 3 units to the left means we subtract 3 from the x-coordinate: \( x' = x - 3 \)
- Moving 5 units down means we subtract 5 from the y-coordinate: \( y' = y - 5 \)
Therefore, the new coordinates \( (x', y') \) will be calculated as:
\[ x' = x - 3 \]
\[ y' = y - 5 \]
Now, since we don't have the original coordinates of points A, B, and C, we cannot compute the new coordinates directly. However, we can check which of the provided answer choices could realistically result from such a translation.
Let's examine the provided answer choices for signs:
- The process of translating points typically increases negative coordinates (as they move "down" in value) and further reduces positive ones.
Checking the answer choices with this observation:
1. **A’(1,0), B’(-1,-4), C’(4,-2)** - Here you have varying changes, but generally, they are mixed and unclear.
2. **A’(7,0), B’(5,-4), C’(10,-2)** - These are all positives and would imply an upward movement, contradicting our downward movement.
3. **A’(-1,2), B’(-3,-2), C’(2,0)** - This choice shows negatives and a positive (+2), but it's still potentially valid.
4. **A’(1,10), B’(-1,6), C’(4,7)** - All points are shifted positively, which also contradicts the downward movement.
For a valid translate, we'd expect outputs with consistently minimized coordinates suggesting downward translation should appear negative or reduced significantly in Y-planar movements.
Let's summarize:
- The new coordinates arising from a left side (negative X) and downward (negative Y) shift should indeed reflect negative movements.
Out of the choices examined, **A'(-1,2), B'(-3,-2), C'(2,0)** looks potentially valid as the only choice that holds some required downward elements, while the others don't fit logically with expected outputs post-translation at all.
Thus, **the best candidate is: A’(-1, 2), B’(-3, -2), C’(2, 0)**.