Question
Point z is dilated by a scale factor of 1/2 what is the location of dilated point z
Answers
GPT-4o mini
To find the location of a point \( z \) after it has been dilated by a scale factor of \( \frac{1}{2} \), you first need to know the original coordinates of point \( z \). Let's say point \( z \) is located at the coordinates \( (x, y) \).
When dilating a point from the origin (0, 0) by a scale factor \( k \), the new coordinates \( (x', y') \) can be found using the following formulas:
\[
x' = k \cdot x
\]
\[
y' = k \cdot y
\]
In this case, with a scale factor of \( \frac{1}{2} \):
\[
x' = \frac{1}{2} \cdot x
\]
\[
y' = \frac{1}{2} \cdot y
\]
Thus, the new coordinates of the dilated point \( z \) will be:
\[
(x', y') = \left(\frac{1}{2}x, \frac{1}{2}y\right)
\]
If you provide the original coordinates of point \( z \), I can give you the specific coordinates of the dilated point.
When dilating a point from the origin (0, 0) by a scale factor \( k \), the new coordinates \( (x', y') \) can be found using the following formulas:
\[
x' = k \cdot x
\]
\[
y' = k \cdot y
\]
In this case, with a scale factor of \( \frac{1}{2} \):
\[
x' = \frac{1}{2} \cdot x
\]
\[
y' = \frac{1}{2} \cdot y
\]
Thus, the new coordinates of the dilated point \( z \) will be:
\[
(x', y') = \left(\frac{1}{2}x, \frac{1}{2}y\right)
\]
If you provide the original coordinates of point \( z \), I can give you the specific coordinates of the dilated point.