quadrilateral \( A B C D, \angle A B C \) is a right angle and \( A B=4 \) units. Quadrilateral \( A B C D \) is dilated by a scale factor of 2 with point \( B \) as the center of tilation, resulting in the image, quadrilateral \( A^{\prime} B^{\prime} C^{\prime} D \). Which statement is true? A. \( \overline{A^{\prime} B^{\prime}} \) is 8 units long and lies on the same line as \( \overline{A B} \). B. \( \overline{A^{\prime} B^{\prime}} \) is 6 units long and lies on the same line as \( \overline{A B} \sqrt[l m]{7} \). C. \( \overline{A^{\prime} B^{\prime}} \) is 8 units long but lies on a different line than \( \overline{A B} \). D. \( \overline{A^{\prime} B^{\prime}} \) is 6 units long but lies on a different line than \( \overline{A B} \).
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Mind Expander
When dilating a figure from a point, each line segment extending from that point is multiplied by the scale factor. Since \( \overline{AB} = 4 \) units and the scale factor is 2, we can calculate the new length \( \overline{A'B'} \) as follows: \( 4 \times 2 = 8 \) units. Furthermore, because the dilation is centered at point \( B \), the line segment \( \overline{A'B'} \) remains on the same line as \( \overline{AB} \). Thus, the correct statement is A. \( \overline{A^{\prime} B^{\prime}} \) is 8 units long and lies on the same line as \( \overline{A B} \).
