2000 AMC 12 Problems/Problem 10
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Problem
The point 
is reflected in the 
-plane, then its image 
is rotated by 
about the 
-axis to produce 
, and finally, is translated by 5 units in the positive-
direction to produce 
. What are the coordinates of ?
Solution
Step 1: Reflect in the xy plane. That is the same as creating the additive inverse of z and sticking it into the z coordinate. (1,2,-3)
Step 2: Rotate around x-axis 180 degrees. That is the same as taking the additive inverse of y and sticking it in the y coordinate, then taking the additive inverse of z and sticking it into the z coordinate. (1, -2, 3)
Step 3: Translate 5 units in positive-y direction. That is the same as adding 5 to y and sticking it in the y coordinate. (1,3,3) 
See Also
| 2000 AMC 12 (Problems • Resources) | ||
| Preceded by Problem 9 | Followed by Problem 11 | |
| 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 | ||
