Math  /  Geometry

QuestionTriangle ABCA B C is dilated to produce triangle ABCA^{\prime} B^{\prime} C^{\prime}.
Determine the scale factor used to create the image. 13\frac{1}{3}

Studdy Solution
Calculate the scale factor using the coordinates of corresponding vertices.
- For vertex AA to AA': $ \text{Scale factor} = \frac{x_{A'}}{x_A} = \frac{1}{3} \]
- For vertex BB to BB': $ \text{Scale factor} = \frac{x_{B'}}{x_B} = \frac{4}{12} = \frac{1}{3} \]
- For vertex CC to CC': $ \text{Scale factor} = \frac{y_{C'}}{y_C} = \frac{4}{12} = \frac{1}{3} \]
Since all calculations yield the same scale factor, the scale factor is consistent.
The scale factor used to create the image is:
13 \boxed{\frac{1}{3}}

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