Question
A triangle is drawn on a coordinate plane. Dilate the figure with a magnitude of 3 in reference to the origin. What are the coordinates of the new vertices of A′B′C′
?
(1 point)
Responses
A′(1,−2)
, B′(3,6)
, and C′(9,0)
upper A prime left parenthesis 1 comma negative 2 right parenthesis , upper B prime left parenthesis 3 comma 6 right parenthesis , and upper C prime left parenthesis 9 comma 0 right parenthesis
A′(−5,−8)
, B′(−3,0)
, and C′(3,0)
upper A prime left parenthesis negative 5 comma negative 8 right parenthesis , upper B prime left parenthesis negative 3 comma 0 right parenthesis , and upper C prime left parenthesis 3 comma 0 right parenthesis
A′(−23,−53)
, B′(0,1)
, and C′(2,−1)
upper A prime left parenthesis negative Start Fraction 2 over 3 End Fraction comma negative Start Fraction 5 over 3 End Fraction right parenthesis , upper B prime left parenthesis 0 comma 1 right parenthesis , and upper C prime left parenthesis 2 comma negative 1 right parenthesis
A′(−6,−15)
, B′(0,9)
, and C′(18,−9)
?
(1 point)
Responses
A′(1,−2)
, B′(3,6)
, and C′(9,0)
upper A prime left parenthesis 1 comma negative 2 right parenthesis , upper B prime left parenthesis 3 comma 6 right parenthesis , and upper C prime left parenthesis 9 comma 0 right parenthesis
A′(−5,−8)
, B′(−3,0)
, and C′(3,0)
upper A prime left parenthesis negative 5 comma negative 8 right parenthesis , upper B prime left parenthesis negative 3 comma 0 right parenthesis , and upper C prime left parenthesis 3 comma 0 right parenthesis
A′(−23,−53)
, B′(0,1)
, and C′(2,−1)
upper A prime left parenthesis negative Start Fraction 2 over 3 End Fraction comma negative Start Fraction 5 over 3 End Fraction right parenthesis , upper B prime left parenthesis 0 comma 1 right parenthesis , and upper C prime left parenthesis 2 comma negative 1 right parenthesis
A′(−6,−15)
, B′(0,9)
, and C′(18,−9)
Answers
GPT-4o mini
To dilate a triangle with a magnitude of 3 in reference to the origin, we multiply each vertex’s coordinates by 3.
Let's denote the original vertices of the triangle as \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \). After dilation, the new vertices \( A' \), \( B' \), and \( C' \) will be calculated as follows:
\[
A' = (3x_1, 3y_1)
\]
\[
B' = (3x_2, 3y_2)
\]
\[
C' = (3x_3, 3y_3)
\]
Now, we can analyze the options you provided.
To find the correct response, we need the original coordinates of the triangle vertices in order to calculate the dilated coordinates. Since the original coordinates are not provided in your question, we cannot directly calculate the new coordinates.
If you know the original vertices, please share them to perform the dilation accurately. If you need help with any other questions or a specific original triangle, please let me know!
Let's denote the original vertices of the triangle as \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \). After dilation, the new vertices \( A' \), \( B' \), and \( C' \) will be calculated as follows:
\[
A' = (3x_1, 3y_1)
\]
\[
B' = (3x_2, 3y_2)
\]
\[
C' = (3x_3, 3y_3)
\]
Now, we can analyze the options you provided.
To find the correct response, we need the original coordinates of the triangle vertices in order to calculate the dilated coordinates. Since the original coordinates are not provided in your question, we cannot directly calculate the new coordinates.
If you know the original vertices, please share them to perform the dilation accurately. If you need help with any other questions or a specific original triangle, please let me know!