Difference between revisions of "2015 AMC 10B Problems/Problem 8"
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==Problem== | ==Problem== | ||
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The letter F shown below is rotated <math>90^\circ</math> clockwise around the origin, then reflected in the <math>y</math>-axis, and then rotated a half turn around the origin. What is the final image? | The letter F shown below is rotated <math>90^\circ</math> clockwise around the origin, then reflected in the <math>y</math>-axis, and then rotated a half turn around the origin. What is the final image? | ||
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==Solution== | ==Solution== | ||
| + | The first rotation moves the base of the <math>F</math> to the negative <math>y</math>-axis, and the stem to the positive <math>x</math>-axis. The reflection then moves the stem to the negative <math>x</math>-axis, with the base unchanged. Then the half turn moves the stem to the positive <math>x</math> axis and the base to the positive <math>y</math>-axis, choice <math>\boxed{\mathbf{(E)}}</math>. | ||
| + | |||
| + | ==Video Solution 1== | ||
| + | https://youtu.be/7xNEFHS7u1U | ||
| − | + | ~Education, the Study of Everything | |
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/mYMfgQ0EuiY | ||
| + | |||
| + | ~savannahsolver | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC10 box|year=2015|ab=B|num-b=7|num-a=9}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 16:12, 2 August 2022
Problem
The letter F shown below is rotated 
clockwise around the origin, then reflected in the 
-axis, and then rotated a half turn around the origin. What is the final image?
Solution
The first rotation moves the base of the 
to the negative -axis, and the stem to the positive 
-axis. The reflection then moves the stem to the negative -axis, with the base unchanged. Then the half turn moves the stem to the positive axis and the base to the positive -axis, choice 
.
Video Solution 1
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 2015 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
