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′(−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)
upper A prime left parenthesis negative 6 comma negative 15 right parenthesis , upper B prime left parenthesis 0 comma 9 right parenthesis , and upper C prime left parenthesis 18 comma negative 9 right parenthesis
A′(−5,−8)
, B′(−3,0)
, and C′(3,0)
?
(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′(−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)
upper A prime left parenthesis negative 6 comma negative 15 right parenthesis , upper B prime left parenthesis 0 comma 9 right parenthesis , and upper C prime left parenthesis 18 comma negative 9 right parenthesis
A′(−5,−8)
, B′(−3,0)
, and C′(3,0)
Answers
GPT-4o mini
To dilate a triangle (or any figure) by a factor of 3 in reference to the origin, we multiply the coordinates of each vertex by the dilation factor.
Let's assume the original coordinates of the triangle's vertices A, B, and C are given by:
- \( A(x_1, y_1) \)
- \( B(x_2, y_2) \)
- \( C(x_3, y_3) \)
The coordinates of the new vertices after dilating by a factor of 3 will be:
- \( A'(3 \cdot x_1, 3 \cdot y_1) \)
- \( B'(3 \cdot x_2, 3 \cdot y_2) \)
- \( C'(3 \cdot x_3, 3 \cdot y_3) \)
Since the original coordinates of the vertices were not provided in your question, I cannot calculate specific coordinates for \( A' \), \( B' \), and \( C' \). However, please check the listed options to see if any of them match the dilated coordinates based on the original coordinates you have.
If you provide the coordinates of the original vertices A, B, and C, I can help you find the correct dilated coordinates.
Let's assume the original coordinates of the triangle's vertices A, B, and C are given by:
- \( A(x_1, y_1) \)
- \( B(x_2, y_2) \)
- \( C(x_3, y_3) \)
The coordinates of the new vertices after dilating by a factor of 3 will be:
- \( A'(3 \cdot x_1, 3 \cdot y_1) \)
- \( B'(3 \cdot x_2, 3 \cdot y_2) \)
- \( C'(3 \cdot x_3, 3 \cdot y_3) \)
Since the original coordinates of the vertices were not provided in your question, I cannot calculate specific coordinates for \( A' \), \( B' \), and \( C' \). However, please check the listed options to see if any of them match the dilated coordinates based on the original coordinates you have.
If you provide the coordinates of the original vertices A, B, and C, I can help you find the correct dilated coordinates.
a -2,-5 b0,3 c6,-3
GPT-4o mini
Using the original vertices you provided:
- \( A(-2, -5) \)
- \( B(0, 3) \)
- \( C(6, -3) \)
We will apply a dilation factor of 3 to these points.
1. For point \( A \):
\[
A' = (3 \cdot -2, 3 \cdot -5) = (-6, -15)
\]
2. For point \( B \):
\[
B' = (3 \cdot 0, 3 \cdot 3) = (0, 9)
\]
3. For point \( C \):
\[
C' = (3 \cdot 6, 3 \cdot -3) = (18, -9)
\]
Therefore, after dilating the triangle with a magnitude of 3 in reference to the origin, the new coordinates of the vertices \( A', B', C' \) are:
- \( A'(-6, -15) \)
- \( B'(0, 9) \)
- \( C'(18, -9) \)
From the options you provided, the correct coordinates of the new vertices \( A', B', C' \) are:
- **\( A'(-6, -15) \), \( B'(0, 9) \), and \( C'(18, -9) \)**.
- \( A(-2, -5) \)
- \( B(0, 3) \)
- \( C(6, -3) \)
We will apply a dilation factor of 3 to these points.
1. For point \( A \):
\[
A' = (3 \cdot -2, 3 \cdot -5) = (-6, -15)
\]
2. For point \( B \):
\[
B' = (3 \cdot 0, 3 \cdot 3) = (0, 9)
\]
3. For point \( C \):
\[
C' = (3 \cdot 6, 3 \cdot -3) = (18, -9)
\]
Therefore, after dilating the triangle with a magnitude of 3 in reference to the origin, the new coordinates of the vertices \( A', B', C' \) are:
- \( A'(-6, -15) \)
- \( B'(0, 9) \)
- \( C'(18, -9) \)
From the options you provided, the correct coordinates of the new vertices \( A', B', C' \) are:
- **\( A'(-6, -15) \), \( B'(0, 9) \), and \( C'(18, -9) \)**.