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Question: In the xy-coordinate plane, Δ ABC has vertices at A(1, -2), B(1, 0.5), and C(2, 1) and Δ DEF has vertices at D(4, -3), E(4, 2), and F(6, 3). The triangles are similar because Δ DEF is the image of Δ ABC under a dilation. what is the scale factor
To find the scale factor of the dilation, we first need to find the lengths of corresponding sides in both triangles. Let's find the length of side AB in ΔABC and side DE in ΔDEF. Side AB in ΔABC has the coordinates A(1, -2) and B(1, 0.5). Using the distance formula: AB = √((1 - 1)^2 + (0.5 - (-2))^2) = √((0)^2 + (2.5)^2) = √(6.25) = 2.5 Side DE in ΔDEF has the coordinates D(4, -3) and E(4, 2). Using the distance formula: DE = √((4 - 4)^2 + (2 - (-3))^2) = √((0)^2 + (5)^2) = √(25) = 5 Now let's find the scale factor (k) using the ratio of corresponding side lengths: k = (side length of ΔDEF) / (side length of ΔABC) k = DE / AB = (5) / (2.5) = 2 Therefore, the scale factor of the dilation is 2.
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