2000 AMC 12 Problem 10

Attempt Problem 10 of the 2000 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2000 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

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?

(1, 7, -3)

(-1, 7, -3)

(-1, -2, 8)

(-1, 3, 3)

(1, 3, 3)

Reflecting in the

xy

-plane negates the

z

-coordinate

180^\circ

turn about the

x

-axis negates both the

y

- and

z

-coordinates

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.

Problem 10 in other years