Difference between revisions of "2016 AMC 10A Problems/Problem 16"
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A triangle with vertices <math>A(0, 2)</math>, <math>B(-3, 2)</math>, and <math>C(-3, 0)</math> is reflected about the <math>x</math>-axis, then the image <math>\triangle A'B'C'</math> is rotated counterclockwise about the origin by <math>90^{\circ}</math> to produce <math>\triangle A''B''C''</math>. Which of the following transformations will return <math>\triangle A''B''C''</math> to <math>\triangle ABC</math>? | A triangle with vertices <math>A(0, 2)</math>, <math>B(-3, 2)</math>, and <math>C(-3, 0)</math> is reflected about the <math>x</math>-axis, then the image <math>\triangle A'B'C'</math> is rotated counterclockwise about the origin by <math>90^{\circ}</math> to produce <math>\triangle A''B''C''</math>. Which of the following transformations will return <math>\triangle A''B''C''</math> to <math>\triangle ABC</math>? | ||
Revision as of 13:06, 4 February 2016
Problem
A triangle with vertices ,
, and
is reflected about the
-axis, then the image
is rotated counterclockwise about the origin by
to produce
. Which of the following transformations will return
to
?
counterclockwise rotation about the origin by
.
clockwise rotation about the origin by
.
reflection about the
-axis
reflection about the line
reflection about the
-axis.
Solution
Consider a point . Reflecting it about the
-axis will map it to
, and rotating it counterclockwise about the origin b
will map it to
. The operation that undoes this is reflection about the line
, so the answer is
.
See Also
2016 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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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