Question

A fence to be constructed along the segment parallel to the side of a triangle with the given coordinates if the material cost $52.25 per unit how much will you need to budget in order to construct the fence and explain all the work leading to the solution.

Coordinates:
A (-5,-2), B (-1,6), C (-8,8)

Also please find the Beginning point and Ending point!!


Please explain PLEASE!

Answer 1

The budget to construct the fence parallel to side AB, using the distance formula and a cost of $52.25 per unit, is approximately $466.85. The segment begins at A and ends at B.

To find the length of the segment parallel to side AB in the triangle with coordinates A (-5, -2), B (-1, 6), and C (-8, 8), we'll use the distance formula. For side AB:

`\[ \text{Distance}_(AB) = √((-1 - (-5))^2 + (6 - (-2))^2) \]`

`\[ = √(4^2 + 8^2) \]`

`\[ = √(16 + 64) \]`

`\[ = √(80) \]`

Now, the cost of constructing the fence is $52.25 per unit. Therefore, the budget needed is given by:

`\[ \text{Budget} = \text{Cost per unit} * \text{Distance}_(AB) \]`

`\[ = 52.25 * √(80) \]`

`\[ \approx 52.25 * 8.94 \]`

`\[ \approx 466.845 \]`

So, the budget needed to construct the fence along the segment parallel to side AB is approximately $466.85.

**Beginning Point and Ending Point:**

The beginning point is A (-5, -2), and the ending point is B (-1, 6) because we are constructing the fence along the segment parallel to side AB.