Math  /  Geometry

QuestionMathXL for School: Practice and Problem-Solving
Points AA^{\prime} and BB^{\prime} are images of points AA and BB after a 270270^{\circ} rotation about the origin. If the slope of ABundefined\overrightarrow{A B} is -3 , what is the slope of ABundefined\widehat{A^{\prime} B^{\prime}} ? Explain.
Select the correct choice below and fill in the answer box to complete your chaice. A. A rotation of 270270^{\circ} would result in a line parallel to ABundefined\overrightarrow{A B}. Since the slopes of parallel lines are equal, the slope of ABundefined\overrightarrow{\mathrm{A}^{\prime} B^{\prime}} is \square 1. B. A rotation of 270270^{\circ} would result in a line perpendicular to ABundefined\overrightarrow{\mathrm{AB}}. Since the slopes of perpendicular lines are opposite reciprocals, the slope of ABundefined\overrightarrow{\mathrm{A}^{\prime} \mathrm{B}^{\prime}} is \square . C. A rotation of 270270^{\circ} would result in a line perpendicular to ABundefined\overrightarrow{A B}. Since the slopes of perpendicular lines are equal, the slope of ABundefined\overrightarrow{A^{\prime} B} is \square . D. A rotation of 270270^{\circ} would result in a line parallel to ABundefined\overrightarrow{A B}. Since the slopes of parallel lines are opposite reciprocals, the slope of ABundefined\overrightarrow{A^{\prime} B} is \square

Studdy Solution
Choose the correct answer based on the relationship:
Since a 270270^\circ rotation results in a line perpendicular to the original, and the slopes of perpendicular lines are opposite reciprocals, the correct choice is:
B. A rotation of 270270^\circ would result in a line perpendicular to ABundefined\overrightarrow{\mathrm{AB}}. Since the slopes of perpendicular lines are opposite reciprocals, the slope of ABundefined\overrightarrow{\mathrm{A}^{\prime} \mathrm{B}^{\prime}} is 13\frac{1}{3}.
The slope of ABundefined\overrightarrow{A^{\prime}B^{\prime}} is:
13 \boxed{\frac{1}{3}}

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