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Difference between revisions of "2019 AMC 10B Problems/Problem 5"
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Don't go breaking my heart
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==Problem==
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Triangle <math>ABC</math> lies in the first quadrant. Points <math>A</math>, <math>B</math>, and <math>C</math> are reflected across the line <math>y=x</math> to points <math>A'</math>, <math>B'</math>, and <math>C'</math>, respectively. Assume that none of the vertices of the triangle lie on the line <math>y=x</math>. Which of the following statements is not always true?
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<math>\textbf{(A) } </math> Triangle <math>A'B'C'</math> lies in the first quadrant.
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<math>\textbf{(B) } </math> Triangles <math>ABC</math> and <math>A'B'C'</math> have the same area.
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<math>\textbf{(C) } </math> The slope of line <math>AA'</math> is <math>-1</math>.
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<math>\textbf{(D) } </math> The slopes of lines <math>AA'</math> and <math>CC'</math> are the same.
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<math>\textbf{(E) } </math> Lines <math>AB</math> and <math>A'B'</math> are perpendicular to each other.
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==Solution==
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==See Also==
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{{AMC10 box|year=2019|ab=B|num-b=4|num-a=6}}
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{{MAA Notice}}

Revision as of 15:32, 14 February 2019

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 (Problems • Answer Key • Resources)
Preceded by
Problem 4 		Followed by
Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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