Find distance

Question

a taxicab avoids traffic by traveling south 5km and then turning and traveling 8 km west and finally turning and traveling 1 km north. how far would the taxicab have traveled if it had taken a straight line between these points.

Answer 1

                                                           ↓

                                                           ↓

                                                           ↓  5

                                                           ↓

                           1 ↑                            ↓

                              ← ← ← ← ← ← ← ←

                                            8

 

Use the Pythagorean Theory to solve for the hypotenuse from the point at the tip of going N 1 to the very beginning.  Note the length of the y leg is one less than 5.  So you have x^2 + y^2 = c^2, where you are solving for c.