Honors Geometry Companion Book, Volume 1

1.1.2 Measuring and Constructing Segments (continued) Example 4 Travel Application

The given information is organized on a series of segments, where the outermost endpoints represent Prof. Burger’s workplace, W , and his home, H . It is given that the distance from W to H is 3 kilometers and the distance from H to the party, M , is 900 meters. Notice that units of these two distances are different: kilometers (km) and meters (m). Only one unit can be used in calculations, so convert either 3 km to meters by multiplying, or 900 m to kilometers by dividing. Because multiplication is usually easier than division, convert the kilometers to meters using the fact that there are 1000 meters in 1 kilometer. WH = 3 km = 3(1000 m) = 3000 m Since M is between W and H in the segment, by the Segment Addition Postulate WM + MH = WH . Substitute the given lengths MH = 900 and WH = 3000 into the equation and solve to find WM . Now use the fact that G is the midpoint of WM to find GM . GM = WM /2 = 2100/2 = 1050 m The distance from the gas station, G to H , is GH = GM + MH = 1050 + 900 = 1950 m.


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