Question

Jeff is traveling from Atlanta to Columbia and then to Charleston. He decides to plot the cities on a coordinate plane. He puts Atlanta at (0, 0), Columbia at (21, 0) and Charleston at (24, -11). He lets each tick mark represent 10 miles. Which formula would correctly give the distance from Atlanta to Charleston?

Answer 1

One formula would be:
$10\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ 10\sqrt{(-11-0)^2+(24-0)^2}$

This is based on the distance formula.  The 10 in front of it is due to the fact that each tick mark is 10 miles; the formula itself will give us the number of units.  Since each unit is worth 10 miles, we must multiply by 10 to find the number of miles.

Answer 2

The answer is (square root sign: 3^2 + (-11)^2)