Answer to Question #159072 in Analytic Geometry for Tyren Penny

Question

You have marked off your shop floor in a grid of 1 foot squares and labeled them with Cartesian coordinates. To perform one task, a worker must go from point (2,7) to point (4,5) then to point (10,6), then back to point (2,7). The worker walks in a straight line between points. How far does she have to walk? 

Answer 1

$AB = \sqrt{(4 - 2)^2 + (5 - 7)^2} = 2\sqrt{2} ≈ 2.8 ft$

$BC = \sqrt{(10 - 4)^2 + (6 - 5)^2} = \sqrt{37} ≈ 6 ft$

$CA = \sqrt{(2 - 10)^2 + (7 - 6)^2} = \sqrt{65} ≈ 8 ft$

Answer: S ≈ 16.8 ≈ 17 ft