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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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1 answer

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!