1992 AMC 12 Problem 3

Attempt Problem 3 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).

m\gt0

and the points

(m,3)

and

(1,m)

lie on a line with slope

m,

then

m=

1

\sqrt2

\sqrt3

2

\sqrt5

Write the slope between the two given points

Set

\frac{m-3}{1-m}=m

and use the positivity condition

The slope condition gives

\frac{m-3}{1-m}=m.

Therefore

m-3=m-m^2,

m^2=3.

Since

m\gt0,

we obtain

m=\sqrt3.

Thus the correct answer is C.

Problem 3 in other years