1992 AMC 12 Problem 12

Attempt Problem 12 of the 1992 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 1992 AMC 12 solutions, or check the answer key.

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

12.

Let

y=mx+b

be the image when the line

x-3y+11=0

is reflected across the

x

-axis. The value of

m+b

-6

-5

-4

-3

-2

Reflection across the

x

-axis replaces each

y

-coordinate by its negative

Replace

y

-y

in the original equation, then solve for

y

A point

(x,y)

is on the reflected line exactly when

(x,-y)

is on the original line. Hence

x+3y+11=0,

y=-\frac13x-\frac{11}{3}.

Therefore

m+b=-\frac13-\frac{11}{3}=-4.

Thus the correct answer is C.

Problem 12 in other years