MathDB

Consider two mirrors placed at a right angle to each other and two points A at

(x,y)

and B at

(a,b)

. Suppose a person standing at point A shines a laser pointer so that it hits both mirrors and then hits a person standing at point B (as shown in the picture). What is the total distance that the light ray travels, in terms of

a

b

x

, and

y

? Assume that

x

y

a

, and

b

are positive. [asy]draw((0,4)--(0,0)--(4,0),linewidth(1)); draw((1,3)--(0,2),MidArrow); draw((0,2)--(2,0),MidArrow); draw((2,0)--(3,1),MidArrow); dot((1,3)); dot((3,1)); label("

A (x,y)

", (1,3),NE); label("

B (a,b)

", (3,1),NE);[/asy]

Problem Statement