Question

A city planner designs a park that is a quadrilateral with vertices at J(-1, 1), K (3, 3), L (5, -1), and

M(-1,-1). There is an entrance to the park at the midpoint of each side of the park. A straight path
connects each entrance to the entrance on the opposite side. Assuming each unit of the coordinate plane
represents 10 meters, what is the total length of the paths to the nearest meter? Round your answer to
the nearest whole number.
The total length of the paths is approximately
meters.

Answer 1

9514 1404 393

Answer:

83 m

Explanation:

The attached diagram shows the lengths of the midlines to be 3.16 and 5.10 units on the coordinate plane. The sum of these is (3.16 +5.10) = 8.26 coordinate plane units. Since each unit on the coordinate plane represents 10 m, the total path length is about ...

8.26(10 m) = 82.6 m ≈ 83 m

_____

The distance formula will tell you the distances are ...

AC = √(3² +1²) = √10

BD = √(5² +1²) = √26

The total path length is about (10 m)(√10 +√26) ≈ 82.61230 m ≈ 83 m.