Question
1 < Suppose the parallelogram on the coordinate plane was dilated with respect to the origin using a magnitude of 1/2 . What would be the coordinates of vertex D'
vertex D is 2, -2
vertex D is 2, -2
Answers
Answer
what would be the coordinates of vertex B' of the parallelogram if it were dilated with respect to the origin using a magnitude of 3?
vertex B is -4, 3
vertex B is -4, 3
Answered by
GPT-4o mini
To find the coordinates of vertex D' after dilating vertex D with respect to the origin using a magnitude of \( \frac{1}{2} \), we will use the following formula for dilation:
\[
(x', y') = \left(k \cdot x, k \cdot y\right)
\]
where \( (x, y) \) are the original coordinates, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the dilation factor.
Here, the original coordinates of vertex D are \( (2, -2) \) and the dilation factor \( k \) is \( \frac{1}{2} \).
Now, apply the dilation:
\[
x' = \frac{1}{2} \cdot 2 = 1
\]
\[
y' = \frac{1}{2} \cdot (-2) = -1
\]
Thus, the new coordinates of vertex D' after the dilation would be:
\[
D' = (1, -1)
\]
So, the coordinates of vertex D' are \( (1, -1) \).
\[
(x', y') = \left(k \cdot x, k \cdot y\right)
\]
where \( (x, y) \) are the original coordinates, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the dilation factor.
Here, the original coordinates of vertex D are \( (2, -2) \) and the dilation factor \( k \) is \( \frac{1}{2} \).
Now, apply the dilation:
\[
x' = \frac{1}{2} \cdot 2 = 1
\]
\[
y' = \frac{1}{2} \cdot (-2) = -1
\]
Thus, the new coordinates of vertex D' after the dilation would be:
\[
D' = (1, -1)
\]
So, the coordinates of vertex D' are \( (1, -1) \).
Answered by
GPT-4o mini
To find the coordinates of vertex B' after dilating vertex B with respect to the origin using a magnitude of \( 3 \), we will again apply the dilation formula:
\[
(x', y') = \left(k \cdot x, k \cdot y\right)
\]
where \( (x, y) \) are the original coordinates, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the dilation factor.
Here, the original coordinates of vertex B are \( (-4, 3) \) and the dilation factor \( k \) is \( 3 \).
Now, apply the dilation:
1. For the \( x \)-coordinate:
\[
x' = 3 \cdot (-4) = -12
\]
2. For the \( y \)-coordinate:
\[
y' = 3 \cdot 3 = 9
\]
Thus, the new coordinates of vertex B' after the dilation would be:
\[
B' = (-12, 9)
\]
So, the coordinates of vertex B' are \( (-12, 9) \).
\[
(x', y') = \left(k \cdot x, k \cdot y\right)
\]
where \( (x, y) \) are the original coordinates, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the dilation factor.
Here, the original coordinates of vertex B are \( (-4, 3) \) and the dilation factor \( k \) is \( 3 \).
Now, apply the dilation:
1. For the \( x \)-coordinate:
\[
x' = 3 \cdot (-4) = -12
\]
2. For the \( y \)-coordinate:
\[
y' = 3 \cdot 3 = 9
\]
Thus, the new coordinates of vertex B' after the dilation would be:
\[
B' = (-12, 9)
\]
So, the coordinates of vertex B' are \( (-12, 9) \).
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