Question

Use the image to answer the question.

A coordinate plane's axes range from negative 3 to 7 by 1-unit increments. 3 points are plotted and joined by solid lines. The points are labeled upper A, upper B, and upper C.

AC¯¯¯¯¯¯¯¯
is a dilation of AB¯¯¯¯¯¯¯¯
, with point B
as the center of dilation. Determine the scale factor.

(1 point)
The scale factor is
.
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Answer 1

To determine the scale factor for the dilation from line segment AB to line segment AC with point B as the center of dilation, you need the coordinates of points A, B, and C.

1. **Identify Coordinates**:
- Let's assume the coordinates of the points based on your description are as follows:
- A(x1, y1)
- B(x2, y2)
- C(x3, y3)

2. **Calculate Distances**:
- Find the length of segment AB:
\[
AB = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}
\]
- Find the length of segment AC:
\[
AC = \sqrt{(x3 - x2)^2 + (y3 - y2)^2}
\]

3. **Calculate Scale Factor**:
- The scale factor (k) can be calculated with the formula:
\[
k = \frac{AC}{AB}
\]

Without the specific coordinates of points A, B, and C, I can't calculate the exact scale factor. If you provide those coordinates, I can help you compute the scale factor. If you have a representation of these points from the image or any specific lengths or distances given, please share, and I can assist you further!