Difference between revisions of "2019 AMC 12B Problems/Problem 3"
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<math>\textbf{(B) } </math> counterclockwise rotation around the origin by <math>90^{\circ}</math> | <math>\textbf{(B) } </math> counterclockwise rotation around the origin by <math>90^{\circ}</math> | ||
− | <math>\textbf{(C) } </math> translation by 3 units to the right and 5 units down | + | <math>\textbf{(C) } </math> translation by <math>3</math> units to the right and <math>5</math> units down |
<math>\textbf{(D) } </math> reflection in the <math>x</math>-axis | <math>\textbf{(D) } </math> reflection in the <math>x</math>-axis |
Revision as of 19:33, 18 February 2019
Problem
Which of the following rigid transformations (isometries) maps the line segment onto the line segment
so that the image of
is
and the image of
is
?
reflection in the
-axis
counterclockwise rotation around the origin by
translation by
units to the right and
units down
reflection in the
-axis
clockwise rotation about the origin by
Solution
We can simply graph the points, or use coordinate geometry, to realize that both and
are, respectively, obtained by rotating
and
by
about the origin. Hence the rotation by
about the origin maps the line segment
to the line segment
, so the answer is
.
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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