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

Answer:

6 miles

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:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Hence:

$AB=\sqrt{( 0.25-(-0.25))^2+(-1.25-(-1.25))^2}=\sqrt{0+0.5^2}=0.5\\ \\BC =\sqrt{(1.25-(-1.25))^2+( 0.25-0.25)^2}=\sqrt{2.5^2+0}=2.5$

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