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Difference between revisions of "2019 AMC 12B Problems/Problem 3"
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Which of the following rigid transformations (isometries) maps the line segment <math>\overline{AB}</math> onto the line segment <math>\overline{A'B'}</math> so that the image of <math>A(-2, 1)</math> is <math>A'(2, -1)</math> and the image of <math>B(-1, 4)</math> is <math>B'(1, -4)</math>?
 
Which of the following rigid transformations (isometries) maps the line segment <math>\overline{AB}</math> onto the line segment <math>\overline{A'B'}</math> so that the image of <math>A(-2, 1)</math> is <math>A'(2, -1)</math> and the image of <math>B(-1, 4)</math> is <math>B'(1, -4)</math>?
  
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(A) reflection in the <math>y</math>-axis
+
<math>\textbf{(A) } </math> reflection in the <math>y</math>-axis
  
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(B) counterclockwise rotation around the origin by <math>90^\circ</math>
+
<math>\textbf{(B) } </math> counterclockwise rotation around the origin by <math>90^{\circ}</math>
  
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(C) translation by <math>3</math> units to the right and <math>5</math> units down
+
<math>\textbf{(C) } </math> translation by 3 units to the right and 5 units down
  
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(D) reflection in the <math>x</math>-axis
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<math>\textbf{(D) } </math> reflection in the <math>x</math>-axis
  
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(E) clockwise rotation around the origin by <math>180^\circ</math>
+
<math>\textbf{(E) } </math> clockwise rotation about the origin by <math>180^{\circ}</math>
  
 
==Solution==
 
==Solution==

Revision as of 14:30, 14 February 2019

Problem

Which of the following rigid transformations (isometries) maps the line segment $\overline{AB}$ onto the line segment $\overline{A'B'}$ so that the image of $A(-2, 1)$ is $A'(2, -1)$ and the image of $B(-1, 4)$ is $B'(1, -4)$?

$\textbf{(A) }$ reflection in the $y$-axis

$\textbf{(B) }$ counterclockwise rotation around the origin by $90^{\circ}$

$\textbf{(C) }$ translation by 3 units to the right and 5 units down

$\textbf{(D) }$ reflection in the $x$-axis

$\textbf{(E) }$ clockwise rotation about the origin by $180^{\circ}$

Solution

See Also

2019 AMC 12B (Problems • Answer Key • Resources)
Preceded by
Problem 2 		Followed by
Problem 4
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 12 Problems and Solutions

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