Question

A town planner lays out the design for a park on a coordinate grid. The point (1, 1) represents a point 1 foot north and 1 foot east of the center of the park at (0, 0). On the design, a triangular path within the park has vertices at (-350, 200), (300, -400), and (160, 500). What is the length of the triangular path, rounded to the nearest tenth of a foot?

Answer 1

9514 1404 393

Answer:

2387.1 ft

Explanation:

I find a spreadsheet to be a convenient tool for repeated calculations using the same formula. Here, the distance between two points is given by ...

d = √((x2 -x1)² +(y2 -y1)²)

For example, the distance between the first two points is ...

d = √((300 -(-350))² +(-400 -200)²) = √(422500 +360000) ≈ 884.59

Other distances are calculated the same way. The results are shown in the attached spreadsheet, which also adds them up.

The path length is 2387.1 feet.