Question

Central Park in New York City is shaped like a rectangle. On a map of the park in the coordinate plane, three of the vertices are located at (-1.25,-0.25) (-1.25, 0.25), and (1.25, 0.25). Distances on the map are in miles. What is the perimeter of Central Park? Show your work.

Answer 1

6 miles

Step-by-step explanation:

Given that the central par is a rectangle with vertices at (-1.25,-0.25) (-1.25, 0.25), and (1.25, 0.25).

Let the vertices be labeled with points ABC, i.e

A (-1.25,-0.25), B(-1.25, 0.25), and C(1.25, 0.25)

The distance between two points is given by the formula:

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Hence:

`AB=√(( 0.25-(-0.25))^2+(-1.25-(-1.25))^2)=√(0+0.5^2)=0.5\\ \\BC =√((1.25-(-1.25))^2+( 0.25-0.25)^2)=√(2.5^2+0)=2.5`

The perimeter of a rectangle is given by:

Perimeter = 2(length + breadth)

Hence, Perimeter = 2(AB + BC)

Perimeter = 2(0.5 + 2.5) = 2(3) = 6

Perimeter = 6 miles