Problem #2353


A triangle with vertices $A(0, 2)$, $B(-3, 2)$, and $C(-3, 0)$ is reflected about the $x$-axis, then the image $\triangle A'B'C'$ is rotated counterclockwise about the origin by $90^{\circ}$ to produce $\triangle A''B''C''$. Which of the following transformations will return $\triangle A''B''C''$ to $\triangle ABC$?

$\textbf{(A)}$ counterclockwise rotation about the origin by $90^{\circ}$.

$\textbf{(B)}$ clockwise rotation about the origin by $90^{\circ}$.

$\textbf{(C)}$ reflection about the $x$-axis

$\textbf{(D)}$ reflection about the line $y = x$

$\textbf{(E)}$ reflection about the $y$-axis.

This problem is copyrighted by the American Mathematics Competitions.

Note: you aren't logged in. If you log in, we'll keep a record of which problems you've solved.

Instructions for entering answers:

  • Reduce fractions to lowest terms and enter in the form 7/9.
  • Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
  • Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
  • Exponents should be entered in the form 10^10.
  • If the problem is multiple choice, enter the appropriate (capital) letter.
  • Enter points with parentheses, like so: (4,5)
  • Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).

For questions or comments, please email

Find out how your skills stack up!

Try our new, free contest math practice test. All new, never-seen-before problems.

AMC/AIME classes

I offer online AMC/AIME classes periodically. Join the mailing list to be informed next time they're offered.

Private coaching is also available.