2019 AMC 10B Problems/Problem 5

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Problem

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.

Solution

See Also

2019 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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