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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
.

1 answer

To determine the scale factor of the dilation from line segment \( \overline{AB} \) to line segment \( \overline{AC} \) with point \( B \) as the center of dilation, you can follow these steps:

  1. Measure the lengths of both segments:

    • Find the distance between points \( A \) and \( B \) to get the length of \( \overline{AB} \).
    • Find the distance between points \( A \) and \( C \) to get the length of \( \overline{AC} \).

  2. Use the formula for the scale factor: \[ \text{Scale factor} = \frac{\text{Length of } \overline{AC}}{\text{Length of } \overline{AB}} \]

  3. Calculate the distances:

    • For example, if \( \overline{AB} \) measures 3 units and \( \overline{AC} \) measures 6 units, then: \[ \text{Scale factor} = \frac{6}{3} = 2 \]

  4. Fill in the answer: Based on your calculations, you would state: The scale factor is \( \text{[calculated value]} \).

Since I can't see the actual image, please calculate the lengths of \( \overline{AB} \) and \( \overline{AC} \) and substitute the values into the formula to find the scale factor.