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: P = 6 miles

Step-by-step explanation: A rectangle is a quadrilateral with opposite sides with the same measure. As Central Park is one, its parallel sides has the same measurement.

Distance of points gives the measurement of the sides of the rectangle. It is calculated as:

$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }$

For the first two points, (-1.25,-0.25) and (-1.25,0.25), note that x-components is the same, so, only y-component is relevant to the distance:

$d=\sqrt{(-1.25+1.25)^{2}+(0.25+0.25)^{2} }$

$d=\sqrt{(0.5)^{2} }$

d = 0.5

Two sides of the rectangle are 0.5 miles.

For points (-1.25,0.25) and (1.25,0.25), y-component will add 0 to the formula. Then,

$d=\sqrt{(1.25+1.25)^{2}+(0.25-0.25)^{2} }$

$d=\sqrt{(2.5)^{2}}$

d = 2.5

Two sides of the park are 2.5 miles.

Perimeter is the sum of all the sides of a geometric figure.

Perimeter of central Park is

P = 0.5+0.5+2.5+2.5

P = 6

Central Park has perimeter of 6 miles.