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Question 4(Multiple Choice Worth 2 points)
(Dilations MC)
Triangle ABC with vertices at A(-3, -3), B(3, 3), C(0, 3) is dilated to create triangle A'B'C' with vertices at A'(-9, -9), B'(9, 9), C'(0, 9). Determine the scale factor used.
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uestion
Question 1 (Answered)
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Respuesta :

GinnyAnswer
To determine the scale factor used in the dilation of triangle ABC to create triangle A'B'C', we can compare the corresponding side lengths of the two triangles. 1. Calculate the original side lengths of triangle ABC: - Side AB: Distance between points A(-3, -3) and B(3, 3) = √[(3 - (-3))^2 + (3 - (-3))^2] = √(6^2 + 6^2) = √(36 + 36) = √72 = 6√2 (approx. 8.49 units) 2. Calculate the corresponding side lengths of triangle A'B'C': - Side A'B': Distance between points A'(-9, -9) and B'(9, 9) = √[(9 - (-9))^2 + (9 - (-9))^2] = √(18^2 + 18^2) = √(324 + 324) = √648 = 18√2 (approx. 25.46 units) 3. Determine the scale factor by comparing the side lengths: - Scale factor = Length of corresponding side in A'B'C' / Length of corresponding side in ABC = 18√2 / 6√2 = 18 / 6 = 3 Therefore, the scale factor used in the dilation from triangle ABC to A'B'C' is 3.

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