The floor plan of a convenience store shows the location at point B of the door and point A if a surveillance camera a mirror is mounted at point c on the opposite wall. how would you find the location of c in order to minimize the distance from A to C to B Aor B orC reflect B across GH or reflect B across DE or Reflect B across EF

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4