Question
determine the scale factor used in the dilation of the line segment ab
Answers
GPT-4o mini
To determine the scale factor used in the dilation of a line segment \( AB \), you typically need two pairs of coordinates: the original endpoints of the segment \( A(x_1, y_1) \) and \( B(x_2, y_2) \), and the coordinates of the dilated endpoints \( A'(x_1', y_1') \) and \( B'(x_2', y_2') \).
The scale factor \( k \) can be calculated using the following formula:
\[
k = \frac{\text{length of } A'B'}{\text{length of } AB}
\]
First, calculate the length of the original segment \( AB \):
\[
\text{length of } AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Then calculate the length of the dilated segment \( A'B' \):
\[
\text{length of } A'B' = \sqrt{(x_2' - x_1')^2 + (y_2' - y_1')^2}
\]
Finally, substitute these lengths into the scale factor equation:
\[
k = \frac{\text{length of } A'B'}{\text{length of } AB}
\]
If you provide the original and dilated coordinates, I can help you compute the scale factor.
The scale factor \( k \) can be calculated using the following formula:
\[
k = \frac{\text{length of } A'B'}{\text{length of } AB}
\]
First, calculate the length of the original segment \( AB \):
\[
\text{length of } AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Then calculate the length of the dilated segment \( A'B' \):
\[
\text{length of } A'B' = \sqrt{(x_2' - x_1')^2 + (y_2' - y_1')^2}
\]
Finally, substitute these lengths into the scale factor equation:
\[
k = \frac{\text{length of } A'B'}{\text{length of } AB}
\]
If you provide the original and dilated coordinates, I can help you compute the scale factor.