1960 AMC 12 Problem 13

Attempt Problem 13 of the 1960 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 1960 AMC 12 solutions, or check the answer key.

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

13.

The polygon(s) formed by

y=3x+2,

y=-3x+2,

and

y=-2,

is (are):

an equilateral triangle

an isosceles triangle

a right triangle

a triangle and a trapezoid

a quadrilateral

Find the three pairwise intersections of the lines

The two slanted lines are mirror images across the

y

-axis

The slanted lines meet at

(0,2),

while their intersections with

y=-2

are

(-\frac{4}{3},-2)

and

(\frac{4}{3},-2).

The latter two points are symmetric about the

y

-axis, so the two slanted sides have equal length. The figure is an isosceles triangle.

Thus, the correct answer is B.

Problem 13 in other years