Difference between revisions of "2000 AMC 12 Problems/Problem 10"

Revision as of 10:13, 7 April 2013

Problem

The point $P = (1,2,3)$ is reflected in the $xy$ -plane, then its image $Q$ is rotated by $180^\circ$ about the $x$ -axis to produce $R$ , and finally, $R$ is translated by 5 units in the positive- $y$ direction to produce $S$ . What are the coordinates of $S$ ?

$\text {(A) } (1,7, - 3) \qquad \text {(B) } ( - 1,7, - 3) \qquad \text {(C) } ( - 1, - 2,8) \qquad \text {(D) } ( - 1,3,3) \qquad \text {(E) } (1,3,3)$

Solution

Step 1: Reflect in the xy plane. Replace z with its additive inverse: $(1,2,-3)$

Step 2: Rotate around x-axis 180 degrees. Replace y and z with their respective additive inverses. $(1, -2, 3)$

Step 3: Translate 5 units in positive-y direction. Replace y with y+5. $(1,3,3) \Rightarrow \text {(E) }$

2000 AMC 12 (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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Difference between revisions of "2000 AMC 12 Problems/Problem 10"

Revision as of 10:13, 7 April 2013

Problem

Solution

See Also