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)
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′(1,0)
, B′(−1,−4)
, C′(4,−2)
upper A prime left parenthesis 1 comma 0 right parenthesis , upper B prime left parenthesis negative 1 comma negative 4 right parenthesis , upper C prime left parenthesis 4 comma negative 2 right parenthesis
A′(−1,2)
, B′(−3,−2)
, C′(2,0)
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′(1,0)
, B′(−1,−4)
, C′(4,−2)
upper A prime left parenthesis 1 comma 0 right parenthesis , upper B prime left parenthesis negative 1 comma negative 4 right parenthesis , upper C prime left parenthesis 4 comma negative 2 right parenthesis
A′(−1,2)
, B′(−3,−2)
, C′(2,0)
Answers
GPT-4o mini
To translate triangle ABC by 3 units to the left and 5 units down, you 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 represented as \( A(x_A, y_A) \), \( B(x_B, y_B) \), and \( C(x_C, y_C) \).
The new coordinates after translation will be:
- \( A'(x_A - 3, y_A - 5) \)
- \( B'(x_B - 3, y_B - 5) \)
- \( C'(x_C - 3, y_C - 5) \)
If we assume the coordinates of the original triangle ABC are:
- \( A(x_A, y_A) \)
- \( B(x_B, y_B) \)
- \( C(x_C, y_C) \)
In order to determine which of the options corresponds to A′B′C′ after the translation, we need the original coordinates. But since they are not provided, we can only analyze the responses to see if they match the pattern of translation.
Given the translation consists of:
- Moving left by 3 (subtracting 3 from the x-coordinate)
- Moving down by 5 (subtracting 5 from the y-coordinate)
We will apply the translation pattern to the given options to check if they follow this method.
Now, let’s analyze the options based on hypothetical original points (since the original coordinates are unknown):
1. **A′(1,10), B′(−1,6), C′(4,7)**:
- These coordinates do not seem to reflect any subtraction consistent with moving 3 left and 5 down. Not a valid option.
2. **A′(7,0), B′(5,−4), C′(10,−2)**:
- Again, these coordinates don't reflect a proper subtractive translation. Not a valid option.
3. **A′(1,0), B′(−1,−4), C′(4,−2)**:
- Again, not following the right subtractive translation. Not valid.
4. **A′(−1,2), B′(−3,−2), C′(2,0)**:
- These coordinates seem reasonable as they could originate from some point (adding back the translation) and reflect the movement needed based on an unknown set of points.
To conclude, without more information, we can't definitively point out the answer, but it seems that option 4 is now the only plausible choice towards a correct transformation if we postulate. If you have the original coordinates of triangle ABC, you can confirm the points correctly.
Let the original coordinates of points A, B, and C be represented as \( A(x_A, y_A) \), \( B(x_B, y_B) \), and \( C(x_C, y_C) \).
The new coordinates after translation will be:
- \( A'(x_A - 3, y_A - 5) \)
- \( B'(x_B - 3, y_B - 5) \)
- \( C'(x_C - 3, y_C - 5) \)
If we assume the coordinates of the original triangle ABC are:
- \( A(x_A, y_A) \)
- \( B(x_B, y_B) \)
- \( C(x_C, y_C) \)
In order to determine which of the options corresponds to A′B′C′ after the translation, we need the original coordinates. But since they are not provided, we can only analyze the responses to see if they match the pattern of translation.
Given the translation consists of:
- Moving left by 3 (subtracting 3 from the x-coordinate)
- Moving down by 5 (subtracting 5 from the y-coordinate)
We will apply the translation pattern to the given options to check if they follow this method.
Now, let’s analyze the options based on hypothetical original points (since the original coordinates are unknown):
1. **A′(1,10), B′(−1,6), C′(4,7)**:
- These coordinates do not seem to reflect any subtraction consistent with moving 3 left and 5 down. Not a valid option.
2. **A′(7,0), B′(5,−4), C′(10,−2)**:
- Again, these coordinates don't reflect a proper subtractive translation. Not a valid option.
3. **A′(1,0), B′(−1,−4), C′(4,−2)**:
- Again, not following the right subtractive translation. Not valid.
4. **A′(−1,2), B′(−3,−2), C′(2,0)**:
- These coordinates seem reasonable as they could originate from some point (adding back the translation) and reflect the movement needed based on an unknown set of points.
To conclude, without more information, we can't definitively point out the answer, but it seems that option 4 is now the only plausible choice towards a correct transformation if we postulate. If you have the original coordinates of triangle ABC, you can confirm the points correctly.
What kind of translation has been made to triangle ABC
?
(1 point)
Responses
Triangle ABC
has been translated 3 units to the right and 6 units down.
Triangle upper A upper B upper C has been translated 3 units to the right and 6 units down.
Triangle ABC
has been translated 3 units to the left and 7 units up.
Triangle upper A upper B upper C has been translated 3 units to the left and 7 units up.
Triangle ABC
has been translated 2 units to the right and 7 units down.
Triangle upper A upper B upper C has been translated 2 units to the right and 7 units down.
Triangle ABC
has been translated 3 units to the right and 7 units down.
?
(1 point)
Responses
Triangle ABC
has been translated 3 units to the right and 6 units down.
Triangle upper A upper B upper C has been translated 3 units to the right and 6 units down.
Triangle ABC
has been translated 3 units to the left and 7 units up.
Triangle upper A upper B upper C has been translated 3 units to the left and 7 units up.
Triangle ABC
has been translated 2 units to the right and 7 units down.
Triangle upper A upper B upper C has been translated 2 units to the right and 7 units down.
Triangle ABC
has been translated 3 units to the right and 7 units down.