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In ΔABC, ∠ ABC is a right angle included between AB = 3 units and BC = 2 units. ΔABC is dilated by a scale factor of 0.5 with point B as the center of dilation, resulting in the image ΔA′B′C′. Which statement about A'B is true? A. A'B is 1.5 units long and lies on the same line as AB . B. A'B is 3 units long and lies on the same line as AB. C. A'B is 1.5 units long but lies on a different line than AB. D. A'B is 3 units long but lies on a different line than AB.

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nobillionaireNobley
A'B' is 1.5 units long and lies on the same line as AB .

Answer:

B. A'B is 1.5 units long and lies on the same line as AB.

Step-by-step explanation:

If AB = 3 units, BC = 2 units and a scale factor of 0.5 is applied, then A'B = 3*0.5 = 1.5 and B'C = 2* 0.5 = 1. Given that the point B is taken as the center of dilation then, segments A'B lies on the same line as AB and B'C lies on the same line as BC.

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