{"status": "success", "data": {"description_md": "Triangle $ABC$ lies in the first quadrant. Points $A$, $B$, and $C$ are reflected across the line $y=x$ to points $A'$, $B'$, and $C'$, respectively. Assume that none of the vertices of the triangle lie on the line $y=x$. Which of the following statements is not always true?\n\n$\\textbf{(A) }$ Triangle $A'B'C'$ lies in the first quadrant.\n$\\textbf{(B) }$ Triangles $ABC$ and $A'B'C'$ have the same area.\n$\\textbf{(C) }$ The slope of line $AA'$ is $-1$.\n$\\textbf{(D) }$ The slopes of lines $AA'$ and $CC'$ are the same.\n$\\textbf{(E) }$ Lines $AB$ and $A'B'$ are perpendicular to each other.", "description_html": "

Triangle ABC lies in the first quadrant. Points A , B , and C are reflected across the line y=x to points A' , B' , and C' , respectively. Assume that none of the vertices of the triangle lie on the line y=x . Which of the following statements is not always true?

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\\textbf{(A) } Triangle A'B'C' lies in the first quadrant.
\n \\textbf{(B) } Triangles ABC and A'B'C' have the same area.
\n \\textbf{(C) } The slope of line AA' is -1 .
\n \\textbf{(D) } The slopes of lines AA' and CC' are the same.
\n \\textbf{(E) } Lines AB and A'B' are perpendicular to each other.

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Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2019 AMC 10B Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10B_p06", "prev": "/problem/19_amc10B_p04"}}