Final answer:
To calculate the cost of constructing the fence, the distance between points A and B was found to be approximately 8.944 units using the distance formula. Multiplying this by the material cost of $52.25 per unit gives a total cost of $467.43. The fence starts at point A and ends at point B.
Step-by-step explanation:
To calculate the cost of constructing a fence parallel to one side of a triangle with given coordinates A (-5,-2), B (-1,6), C (-8,8), we need to first identify which side the fence will be parallel to and then find out the length of that side. Assuming the fence is parallel to the side between points A and B, we use the distance formula to find the length of that segment:
Distance formula: d = √((x2 - x1)² + (y2 - y1)²)
For points A (-5, -2) and B (-1, 6), we calculate as:Plug in the coordinates into the distance formula: d = √((-1 - (-5))² + (6 - (-2))²)Simplify the equation: d = √((4)² + (8)²)Calculate the squares: d = √(16 + 64)Add the squares: d = √(80)Find the square root: d = √(80) ≈ 8.944 unitsNow, we know the length of the fence needed is approximately 8.944 units. If the cost per unit is $52.25, we can then calculate the total cost as:Total cost = length of fence × cost per unitTotal cost = 8.944 units × $52.25 per unitTotal cost = $467.43
Therefore, a budget of $467.43 is required to construct the fence. The beginning point is A and the ending point is B since we've assumed the fence is parallel to AB.