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Difference between revisions of "2019 AMC 10B Problems/Problem 5"
m (Sorry, I keep forgetting that when the answer choices are phrases, I have to leave a full line of space in between them)
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<math>\textbf{(A) } </math> Triangle <math>A'B'C'</math> lies in the first quadrant.
 
<math>\textbf{(A) } </math> Triangle <math>A'B'C'</math> lies in the first quadrant.
 +
 
<math>\textbf{(B) } </math> Triangles <math>ABC</math> and <math>A'B'C'</math> have the same area.
 
<math>\textbf{(B) } </math> Triangles <math>ABC</math> and <math>A'B'C'</math> have the same area.
 +
 
<math>\textbf{(C) } </math> The slope of line <math>AA'</math> is <math>-1</math>.
 
<math>\textbf{(C) } </math> The slope of line <math>AA'</math> is <math>-1</math>.
 +
 
<math>\textbf{(D) } </math> The slopes of lines <math>AA'</math> and <math>CC'</math> are the same.
 
<math>\textbf{(D) } </math> The slopes of lines <math>AA'</math> and <math>CC'</math> are the same.
 +
 
<math>\textbf{(E) } </math> Lines <math>AB</math> and <math>A'B'</math> are perpendicular to each other.
 
<math>\textbf{(E) } </math> Lines <math>AB</math> and <math>A'B'</math> are perpendicular to each other.
  

Revision as of 14:33, 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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