Distance of points on a map

Question

A ferry sets sail from an island located at (4,12) on a map. It's destinations is Ferry Landing B at (6,2). How Far will the ferry travel of each unit on the grid is .5 mile?

Answer 1

This is a pretty complicated question for pre-algebra since you have to use the Pythagorean Theorem to solve it.  If you plot the points (4,12) and (6,2) you will see that the x-coordinates are separated by 2 units (since 6 - 4 = 2) and the y-coordinates are separated by 10 units (since |2 - 12| = 10).  If you plot the point (4,2) and draw the triangle that connects the 3 points you will see that it is a right triangle with the 2 legs having lengths equal to 2 and 10, so by the Pythagorean Theorem the length of the hypotenuse is √(2² + 10²) = √(104) ≅ 10.20 grid units.  Since each grid unit is 0.5 miles the distance travelled is 0.5*10.20 ~ 5.1 miles.