Question

Central Park is shaped like a rectangle. Two diagonally-opposite corners of the park are located at (-9,7) and (4,-3) on the coordinate plane. If each square on the graph represents one city block, what is the perimeter of Central park

Answer 1

Hello!

The answer is:

The perimeter of Central Park is equal to 46 units.

`Perimeter=46units`

Why?

Considering that each block on the graph represents on unit, we need to calculate the length of two sides (base and height) since rectangles has two pairs of equal sides (base and height).

- Calculations for the base:

To calculate the length of the base, we have to find another point that has the same x-cordinate of the second point (4) and the same y-coordinate of the first point (7), we need to do it in order to extend the line of the base, and then, find the distance between those two points. We have that the new point will be (4,7).

Calculating the distance between the points (-9,7) and (4,7) to find the lenght of the base, we have:

`distance=BaseLength=\sqrt{(x_(2)-x_(1))^(2) +(y_(2)-y_(1))^(2)}\\\\distance=BaseLength=\sqrt{(4-(-9))^(2) +(7-7)^(2)}\\\\distance=BaseLength=\sqrt{(13)^(2) +(0)^(2)}=13`

Hence, we have that the base of the rectangle is equal to 13 units.

- Calculations for the height:

Now, to calculate the length of the height, we need to calculate the distance between the point (4,-3) and the new point (4,7)

Calculating the distance between the points (4,-3) and (4,7) to find the lenght of the height, we have:

`distance=HeightLength=\sqrt{(x_(2)-x_(1))^(2) +(y_(2)-y_(1))^(2)}\\\\distance=BaseLength=\sqrt{(4-4)^(2) +(7-(-3))^(2)}\\\\distance=BaseLength=\sqrt{(0)^(2) +(10)^(2)}=10`

Hence, we have that the height of the rectangle is equal to 10 units.

- Perimeter calculations:

We can calculate the perimeter of rectangle using the following formula:

`Perimeter=2b+2h`

Where,

b, is the base of the rectangle

h, is the height of the rectangle

So, calculating the perimeter of the rectangle, we have:

`b=13units`

`h=10units`

`Perimeter=2(13units)+2(10units)=26units+20units=46units`

`Perimeter=46units`

Therefore, the perimeter of Central Park is equal to 46 units.

`Perimeter=46units`

Have a nice day!