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

Answer:

Each side of the fountain is 5 units

Step-by-step 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 = $\sqrt{(x_2-x_1)^2 +(y_2-y_2)^2}$

Now lets find the length of AB

Length of AB = $\sqrt{(x_2-x_1)^2 +(y_2-y_2)^2}$

where

$x_1$ = 7.5

$x_2$ = 11.5

$y_1$ = 5

$y_2$ = 2

Substituting the values we get,

Length of AB = $\sqrt{(11.5 - 7.5)^2 +(5-2)^2}$

Length of AB = $\sqrt{(4)^2 +(3)^2}$

Length of AB = $\sqrt{16 +9}$

Length of AB = $\sqrt{25}$

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