2000 AMC 12 Problem 10

Problem 10 of 25EasierGeometry

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?

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Solution

Reflecting

(1, 2, 3)

in the

xy

-plane gives

Q = (1, 2, -3).

Rotating

180^\circ

about the

x

-axis negates

y

and

z,

giving

R = (1, -2, 3).

Translating

5

units in the positive

y

direction gives

S = (1, 3, 3).

Thus, the correct answer is E.

Tagged: transformation · 3D geometry · coordinate geometry