Final answer:
The perimeter of triangle ABC is found by calculating the distances between its vertices using coordinates A (5,-1), B (-1,1), and C (0,-3) with the distance formula. The lengths of the sides are approximately 6.3, 5.4, and 4.1 units. Summing these gives a perimeter of approximately 15.8 units.
Step-by-step explanation:
To determine the perimeter of triangle ABC, we need to find the lengths of its sides using the coordinates given for the vertices A (5,-1), B (-1,1), and C (0,-3). We calculate the distances between each pair of points using the distance formula: d = √((x2-x1)² + (y2-y1)²). This formula is derived from the Pythagorean theorem, which relates the legs of a right triangle to the length of the hypotenuse.
For each side of the triangle:
- AB: √((5 - (-1))² + ((-1) - 1)²) ≈ √((6)² + (-2)²) ≈ 6.3,
- AC: √((5 - 0)² + ((-1) - (-3))²) ≈ √((5)² + (2)²) ≈ √29 ≈ 5.4, and
- BC: √((-1 - 0)² + (1 - (-3))²) ≈ √((1)² + (4)²) ≈ √17 ≈ 4.1.
Finally, the perimeter of the triangle is the sum of the lengths of these sides, which is approximately 6.3 + 5.4 + 4.1 = 15.8 units.