about how many kilometers?

Question

martin is drawing the path of a boat on a coordinate plane, where 1 unit is equal to 1 kilometer. the boat started from (1,2) and headed northeast until it reached (4,6). the boat then turned and headed northwest until it reaches (0,9). about how many more kilometers did the boat travel than if it would have traveled straight to (0,9) from its starting point?

Answer 1

This is three Pythagorean theorem problems, one for the trip from (1,2) to (4,6), the next for (4,6) to (0,9) and the third for the direct trip from (1,2) to (0,9).  If you draw the points on graph paper you will see that you can construct right triangles with these segments as the hypotenuses.  You then sum up the two first distances and compare that to the final.

 

Alternately, if you do not need an exact answer, you can graph the points using some scale like one inch = 1 kilometer and measure with a ruler and then convert the scale back to kilometers.  If you know the Pythagorean Theorem, though, that is probably what your teacher wants you to use.