Respuesta :
Answer:
In conclusion, the lengths of the sides of Triangle FUN are:
- Side FU: 3√2 units
- Side UN: 4√2 units
- Side NF: 5√2 units
These calculations determine the precise length of each side of the triangle based on the given coordinates of its vertices.
Step-by-step explanation:
To find the lengths of the sides of Triangle FUN with vertices F (-1,3), U (2,6), and N (6,2), we can use the distance formula which calculates the distance between two points in a coordinate plane. The distance formula is √((x₂ - x₁)² + (y₂ - y₁)²).
1. Length of side FU:
- Using the distance formula: √((2 - (-1))² + (6 - 3)²)
- Calculating: √(3² + 3²) = √(9 + 9) = √18 = 3√2
- So, the length of side FU is 3√2 units.
2. Length of side UN:
- Using the distance formula: √((6 - 2)² + (2 - 6)²)
- Calculating: √(4² + (-4)²) = √(16 + 16) = √32 = 4√2
- Therefore, the length of side UN is 4√2 units.
3. Length of side NF:
- Using the distance formula: √((-1 - 6)² + (3 - 2)²)
- Calculating: √((-7)² + 1²) = √(49 + 1) = √50 = 5√2
- Hence, the length of side NF is 5√2 units.
In conclusion, the lengths of the sides of Triangle FUN are:
- Side FU: 3√2 units
- Side UN: 4√2 units
- Side NF: 5√2 units
These calculations determine the precise length of each side of the triangle based on the given coordinates of its vertices.
