Question

EASY 5 POINTS!!!! A new park in the shape of a hexagon will have 66 sides of equal length. On a scale drawing, the coordinates of the vertices of the park are: (6.5,5)6.5,5, (18.5,0)18.5,0, (6.5,-5)6.5,-5,

(-6.5,-5)-6.5,-5, (-18.5,0)-18.5,0, and (-6.5,5)-6.5,5. How long is each side of the park?

Answer 1

To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. By following the steps outlined, you can determine the length of each side of the hexagon.

Step-by-step explanation:

To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. In this case, the coordinates of the vertices of the hexagon form a regular hexagon, meaning all sides are equal in length. Here's how you can find the length of one side:

1. Take the coordinates of two adjacent vertices of the hexagon.
2. Use the distance formula, which is sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
3. Plug in the coordinates and calculate the distance.
4. Repeat the process for different pairs of adjacent vertices to make sure all sides have the same length.

By following these steps, you should be able to determine the length of each side of the hexagon.

Answer 2

To solve this problem, first we have to plot the vertices in a Cartesian plane to know the plot. This would also give us an idea of which points are adjacent or interconnected forming a hexagon.

The plot is shown below. Now we can see which points are adjacent to each other. Let us take points (-6.5, 5) and (6.5, 5) for our calculation.

The distance formula given two points is:

d^2 = (x2 – x1)^2 + (y^2 – y^1)^2

Now we calculate the distance between 2 points:

d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2

d^2 = 169

d = 13

Therefore the length of each side of the park is 13 units.

Answer:

13 units