Barney has to run some errands around town. look at the map below to calculate his distance if he starts at home, goes to the video store, then the grocery store, grabs a fast snack, and ends at home. how many units did he walk? coordinate grid with points labeled home, video store, fast snacks, and grocery store. home is located at negative 3, 4, video store is at 4, 4, fast snacks is at negative 3, negative 3, and grocery store is at 4, negative 3.

828. all there is to it!

here, if you ever need with rounding (or other forms of arithmetic/math) again, use this:

thats the rounding one, but if you just click the top left, it shows you all the calculators you may need!

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