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2019 AMC 10B Question 5

AMC10 · 2019 AMC 10B

Question 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?
  1. Triangle $A'B'C'$ lies in the first quadrant.
  2. Triangles $ABC$ and $A'B'C'$ have the same area.
  3. The slope of line $AA'$ is $-1.$
  4. The slopes of lines $AA'$ and $CC'$ are the same.
  5. Lines $AB$ and $A'B'$ are perpendicular to
    each other.