Question
Use the image to answer the question.
Quadrilateral A B C D is on a coordinate plane. The vertices are A at negative 1 comma 1, B at 1 comma 2, C at 3 comma 0, and D at 1 comma negative 1.
Identify the coordinates of the image of quadrilateral ABCD
after a dilation by a scale factor of 4 centered at the origin.
(2 points)
A′
(
), B′
(
), C′
(
), D′
(
)
Quadrilateral A B C D is on a coordinate plane. The vertices are A at negative 1 comma 1, B at 1 comma 2, C at 3 comma 0, and D at 1 comma negative 1.
Identify the coordinates of the image of quadrilateral ABCD
after a dilation by a scale factor of 4 centered at the origin.
(2 points)
A′
(
), B′
(
), C′
(
), D′
(
)
Answers
Answered by
GPT-4o mini
To find the coordinates of the image of quadrilateral ABCD after a dilation by a scale factor of 4 centered at the origin, we multiply each coordinate of the vertices by the scale factor.
The original coordinates are:
- A (-1, 1)
- B (1, 2)
- C (3, 0)
- D (1, -1)
Now, applying the dilation:
1. For A (-1, 1):
\[
A' = (4 \cdot -1, 4 \cdot 1) = (-4, 4)
\]
2. For B (1, 2):
\[
B' = (4 \cdot 1, 4 \cdot 2) = (4, 8)
\]
3. For C (3, 0):
\[
C' = (4 \cdot 3, 4 \cdot 0) = (12, 0)
\]
4. For D (1, -1):
\[
D' = (4 \cdot 1, 4 \cdot -1) = (4, -4)
\]
Thus, the coordinates of the image of quadrilateral ABCD after dilation are:
- A′ (-4, 4)
- B′ (4, 8)
- C′ (12, 0)
- D′ (4, -4)
Final coordinates:
- A′ (-4, 4)
- B′ (4, 8)
- C′ (12, 0)
- D′ (4, -4)
The original coordinates are:
- A (-1, 1)
- B (1, 2)
- C (3, 0)
- D (1, -1)
Now, applying the dilation:
1. For A (-1, 1):
\[
A' = (4 \cdot -1, 4 \cdot 1) = (-4, 4)
\]
2. For B (1, 2):
\[
B' = (4 \cdot 1, 4 \cdot 2) = (4, 8)
\]
3. For C (3, 0):
\[
C' = (4 \cdot 3, 4 \cdot 0) = (12, 0)
\]
4. For D (1, -1):
\[
D' = (4 \cdot 1, 4 \cdot -1) = (4, -4)
\]
Thus, the coordinates of the image of quadrilateral ABCD after dilation are:
- A′ (-4, 4)
- B′ (4, 8)
- C′ (12, 0)
- D′ (4, -4)
Final coordinates:
- A′ (-4, 4)
- B′ (4, 8)
- C′ (12, 0)
- D′ (4, -4)
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