Question
what dilation is it when A(-4, 3) to E(4.5, 5)
Answers
GPT-4o mini
To determine the dilation factor that transforms point A \((-4, 3)\) to point E \((4.5, 5)\), you can use the formula for dilation centered at the origin. The dilation formula states that:
\[
E = k \cdot A
\]
where \(E\) is the point after dilation, \(A\) is the original point, and \(k\) is the dilation factor.
1. First, calculate the coordinates of point E in terms of point A and the dilation factor \(k\):
- The x-coordinates give us:
\[
4.5 = k \cdot (-4)
\]
- The y-coordinates give us:
\[
5 = k \cdot 3
\]
2. Now we can solve for \(k\) from each equation.
For the x-coordinate:
\[
k = \frac{4.5}{-4} = -1.125
\]
For the y-coordinate:
\[
k = \frac{5}{3} \approx 1.6667
\]
Since the \(k\) values from the x and y coordinates are not equal, this indicates that the transformation is not a uniform dilation centered at the origin.
In this case, it seems that the points are transformed by a linear transformation that involves different scaling factors on the x and y axes.
Thus, if we strictly want to find a single dilation factor, we see there is no consistent \(k\) that would apply to both coordinates. If you have a specific dilation center or transformation you'd like to analyze, please provide that information!
\[
E = k \cdot A
\]
where \(E\) is the point after dilation, \(A\) is the original point, and \(k\) is the dilation factor.
1. First, calculate the coordinates of point E in terms of point A and the dilation factor \(k\):
- The x-coordinates give us:
\[
4.5 = k \cdot (-4)
\]
- The y-coordinates give us:
\[
5 = k \cdot 3
\]
2. Now we can solve for \(k\) from each equation.
For the x-coordinate:
\[
k = \frac{4.5}{-4} = -1.125
\]
For the y-coordinate:
\[
k = \frac{5}{3} \approx 1.6667
\]
Since the \(k\) values from the x and y coordinates are not equal, this indicates that the transformation is not a uniform dilation centered at the origin.
In this case, it seems that the points are transformed by a linear transformation that involves different scaling factors on the x and y axes.
Thus, if we strictly want to find a single dilation factor, we see there is no consistent \(k\) that would apply to both coordinates. If you have a specific dilation center or transformation you'd like to analyze, please provide that information!