Question

A new fountain in the shape of a hexagon will have 6 sides of equal length. On a scale drawing, the coordinates of the vertices of the fountain are: (7.5,5), (11.5,2), (7.5,−1), (2.5,−1), (−1.5,2), and (2.5,5).

How long is each side of the fountain?

Answer 1

5 units

Explanation:

Answer 2

Each side of the fountain is 5 units

Explanation:

Given:

All the sides of the vertices are equal.

Vertices of the fountain

(7.5,5),

(11.5,2),

(7.5,−1),

(2.5,−1),

(−1.5,2),

(2.5,5)

To Find:

Length of the each side of the fountain = ?

Solution:

Let us find the Length of the hexagon using the distance formula

Distance formula =
`√((x_2-x_1)^2 +(y_2-y_2)^2)`

Now lets find the length of AB

Length of AB =
`√((x_2-x_1)^2 +(y_2-y_2)^2)`

where

`x_1` = 7.5

`x_2` = 11.5

`y_1` = 5

`y_2` = 2

Substituting the values we get,

Length of AB =
`√((11.5 - 7.5)^2 +(5-2)^2)`

Length of AB =
`√((4)^2 +(3)^2)`

Length of AB =
`√(16 +9)`

Length of AB =
`√(25)`

Length of AB = 5

Since all the sides of the hexagon are said to be equal, the length of the sides of the hexagon is 5 units