Ab←→ and bc←→ form a right angle at point b. if a = (-3, -1) and
b = (4, 4), what is the equation of bc←→?
x + 3y = 16
2x + y = 12
-7x − 5y = -48
7x − 5y = 48

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

she will travel a distance in the range of 3 - 11 miles