Problem

2019 AMC 10B Problem 5

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?

\textbf{(A) } Triangle A'B'C' lies in the first quadrant.

\textbf{(B) } Triangles ABC and A'B'C' have the same area.

\textbf{(C) } The slope of line AA' is -1.

\textbf{(D) } The slopes of lines AA' and CC' are the same.

\textbf{(E) } Lines AB and A'B' are perpendicular to each other.


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


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