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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. Select the TWO true statements about the transformation of Δ ABC

To determine the true statements about the transformation of Δ ABC, we need to analyze the coordinates and relationships between the vertices of both the triangles. 1. Δ DEF has the same orientation as Δ ABC: Orientation is preserved in similar triangles under dilation. Since both triangles are similar and no rotation or reflection is mentioned, Δ DEF has the same orientation as Δ ABC. 2. The center of dilation is the origin (0, 0): To find the center of dilation, we can compare the coordinates of corresponding vertices. Let's use vertices A and D, and B and E. A (1, -2) to D (4, -3), and B (1, 0.5) to E (4, 2). We can check if the ratio of their coordinates (x and y) is consistent: D's x-coordinate is 4 times A's x-coordinate (4 = 1*4), D's y-coordinate is 1.5 times A's y-coordinate (-3 = -2*1.5), E's x-coordinate is 4 times B's x-coordinate (4 = 1*4), E's y-coordinate is 4 times B's y-coordinate (2 = 0.5*4). Since the ratio of both coordinates is consistent between corresponding points, and this ratio is the same for all such points, we can conclude that the origin (0, 0) is the center of dilation. So, the two true statements about the transformation of Δ ABC are: 1. Δ DEF has the same orientation as Δ ABC. 2. The center of dilation is the origin (0, 0).

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