2019 AMC 12B Problems/Problem 3

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

We can simply graph or use coordinate rules to realize that both $A$ and $B$ are rotated $180^{\circ}$ about the origin, therefore $\overline{AB}$ is rotated $180^{\circ}$ , so $\boxed{(\text{E})}$ -Dodgers66

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

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2019 AMC 12B Problems/Problem 3

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