Given the \( \triangle A B C \) with the points \( A=(-1,3) B=(2,4) C=(4,7) \) and it's dilation, triangle \( A^{\prime} B^{\prime} C^{\prime} \), with points \( A^{\prime}=(-3,9) B^{\prime}=(6,12) C^{\prime}=(12,21) \) what is the scale factor? Select one: a. \( \frac{1}{3} \) b. 2 c. \( \frac{1}{2} \) d. 3
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To find the scale factor of the dilation from triangle \( ABC \) to triangle \( A'B'C' \), we can compare the coordinates of corresponding points. For point \( A \): - The coordinates change from \( A=(-1,3) \) to \( A' = (-3,9) \). - To find the scale factor, we divide the coordinates of \( A' \) by the coordinates of \( A \): - For the x-coordinates: \( \frac{-3}{-1} = 3 \) - For the y-coordinates: \( \frac{9}{3} = 3 \) Repeating this for points \( B \) and \( C \) will yield the same result: - For point \( B \): - \( B=(-2,4) \) to \( B'=(6,12) \) gives \( \frac{6}{2} = 3 \) and \( \frac{12}{4} = 3 \). - For point \( C \): - \( C=(4,7) \) to \( C'=(12,21) \) gives \( \frac{12}{4} = 3 \) and \( \frac{21}{7} = 3 \). Since all comparisons yield a consistent scale factor of 3, the answer is: **d. 3**
