Question
A coordinate plane's x-axis ranges from negative 3 to 9 and its y-axis ranges from negative 2 to 6, both by 1-unit increments. 3 points are marked and plotted forming triangle upper A upper B upper C.
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)
Responses
A′(1,10), B′(−1,6), C′(4,7)
upper A prime left parenthesis 1 comma 10 right parenthesis , upper B prime left parenthesis negative 1 comma 6 right parenthesis , upper C prime left parenthesis 4 comma 7 right parenthesis
A′(7,0), B′(5,−4), C′(10,−2)
upper A prime left parenthesis 7 comma 0 right parenthesis , upper B prime left parenthesis 5 comma negative 4 right parenthesis , upper C prime left parenthesis 10 comma negative 2 right parenthesis
A′(−1,2), B′(−3,−2), C′(2,0)
upper A prime left parenthesis negative 1 comma 2 right parenthesis , upper B prime left parenthesis negative 3 comma negative 2 right parenthesis , upper C prime left parenthesis 2 comma 0 right parenthesis
A′(1,0), B′(−1,−4), C′(4,−2)
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)
Responses
A′(1,10), B′(−1,6), C′(4,7)
upper A prime left parenthesis 1 comma 10 right parenthesis , upper B prime left parenthesis negative 1 comma 6 right parenthesis , upper C prime left parenthesis 4 comma 7 right parenthesis
A′(7,0), B′(5,−4), C′(10,−2)
upper A prime left parenthesis 7 comma 0 right parenthesis , upper B prime left parenthesis 5 comma negative 4 right parenthesis , upper C prime left parenthesis 10 comma negative 2 right parenthesis
A′(−1,2), B′(−3,−2), C′(2,0)
upper A prime left parenthesis negative 1 comma 2 right parenthesis , upper B prime left parenthesis negative 3 comma negative 2 right parenthesis , upper C prime left parenthesis 2 comma 0 right parenthesis
A′(1,0), B′(−1,−4), C′(4,−2)
Answers
GPT-4o mini
To find the new coordinates of triangle A'B'C' after translating triangle ABC by 3 units to the left and 5 units down, we need to apply the following transformations to each vertex of the triangle:
- Subtract 3 from the x-coordinates (to move left)
- Subtract 5 from the y-coordinates (to move down)
Let’s denote the original points as:
- A(x₁, y₁)
- B(x₂, y₂)
- C(x₃, y₃)
The new coordinates will be:
- A'(x₁ - 3, y₁ - 5)
- B'(x₂ - 3, y₂ - 5)
- C'(x₃ - 3, y₃ - 5)
Since we don’t have the original coordinates of points A, B, and C, we cannot calculate the new points directly. However, we can evaluate the given options against the general transformations.
Let's check each provided option against the translations:
1. **Option (A′(1,10), B′(−1,6), C′(4,7))**
- This would mean the original points are:
- A(1 + 3, 10 + 5) = (4, 15)
- B(−1 + 3, 6 + 5) = (2, 11)
- C(4 + 3, 7 + 5) = (7, 12)
2. **Option (A′(7,0), B′(5,−4), C′(10,−2))**
- This would mean the original points are:
- A(7 + 3, 0 + 5) = (10, 5)
- B(5 + 3, -4 + 5) = (8, 1)
- C(10 + 3, -2 + 5) = (13, 3)
3. **Option (A′(−1,2), B′(−3,−2), C′(2,0))**
- This would mean the original points are:
- A(−1 + 3, 2 + 5) = (2, 7)
- B(−3 + 3, −2 + 5) = (0, 3)
- C(2 + 3, 0 + 5) = (5, 5)
4. **Option (A′(1,0), B′(−1,−4), C′(4,−2))**
- This would mean the original points are:
- A(1 + 3, 0 + 5) = (4, 5)
- B(−1 + 3, −4 + 5) = (2, 1)
- C(4 + 3, −2 + 5) = (7, 3)
Since we do not have the original coordinates of triangle ABC, we can't definitively determine which option represents the correctly translated triangle without them. You must check which set of transformed coordinates corresponds to the original triangle coordinates that were plotted.
If there are any original coordinates provided or specific instructions linked to the original triangle definition, please share that information to help determine the correct answer.
- Subtract 3 from the x-coordinates (to move left)
- Subtract 5 from the y-coordinates (to move down)
Let’s denote the original points as:
- A(x₁, y₁)
- B(x₂, y₂)
- C(x₃, y₃)
The new coordinates will be:
- A'(x₁ - 3, y₁ - 5)
- B'(x₂ - 3, y₂ - 5)
- C'(x₃ - 3, y₃ - 5)
Since we don’t have the original coordinates of points A, B, and C, we cannot calculate the new points directly. However, we can evaluate the given options against the general transformations.
Let's check each provided option against the translations:
1. **Option (A′(1,10), B′(−1,6), C′(4,7))**
- This would mean the original points are:
- A(1 + 3, 10 + 5) = (4, 15)
- B(−1 + 3, 6 + 5) = (2, 11)
- C(4 + 3, 7 + 5) = (7, 12)
2. **Option (A′(7,0), B′(5,−4), C′(10,−2))**
- This would mean the original points are:
- A(7 + 3, 0 + 5) = (10, 5)
- B(5 + 3, -4 + 5) = (8, 1)
- C(10 + 3, -2 + 5) = (13, 3)
3. **Option (A′(−1,2), B′(−3,−2), C′(2,0))**
- This would mean the original points are:
- A(−1 + 3, 2 + 5) = (2, 7)
- B(−3 + 3, −2 + 5) = (0, 3)
- C(2 + 3, 0 + 5) = (5, 5)
4. **Option (A′(1,0), B′(−1,−4), C′(4,−2))**
- This would mean the original points are:
- A(1 + 3, 0 + 5) = (4, 5)
- B(−1 + 3, −4 + 5) = (2, 1)
- C(4 + 3, −2 + 5) = (7, 3)
Since we do not have the original coordinates of triangle ABC, we can't definitively determine which option represents the correctly translated triangle without them. You must check which set of transformed coordinates corresponds to the original triangle coordinates that were plotted.
If there are any original coordinates provided or specific instructions linked to the original triangle definition, please share that information to help determine the correct answer.