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/_\A^(')B^(')C^(') is a dilation of /_\ABC. What is the scale factor?

/△A′B′C′_{\triangle}A^{\prime}B^{\prime}C^{\prime} is a dilation of /△ABC_{\triangle}ABC. What is the scale factor?

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Q. /△A′B′C′_{\triangle}A^{\prime}B^{\prime}C^{\prime} is a dilation of /△ABC_{\triangle}ABC. What is the scale factor?
  1. Identify vertices and coordinates: Identify the corresponding vertices and their coordinates in both triangles. Assume coordinates for triangle ABCABC are A(1,1)A(1,1), B(3,1)B(3,1), C(2,3)C(2,3) and for triangle A′B′C′A'B'C' are A′(2,2)A'(2,2), B′(6,2)B'(6,2), C′(4,6)C'(4,6).
  2. Calculate distances for scale factor: Calculate the distances between corresponding vertices in both triangles to find the scale factor. For AA to A′A', distance = (2−1)2+(2−1)2=2\sqrt{(2-1)^2 + (2-1)^2} = \sqrt{2}. For BB to B′B', distance = (6−3)2+(2−1)2=10\sqrt{(6-3)^2 + (2-1)^2} = \sqrt{10}.

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