How do you find the perimeter of triangle ABC with the coordinates A(3, 0), B(0, 4), and C(3, 0)?

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To find the perimeter of triangle ABC with the given coordinates, we follow these steps:

  1. Identify the coordinates: We have the following points for the triangle:
    • A(3, 0)
    • B(0, 4)
    • C(3, 0)
  2. Calculate the lengths of the sides: The perimeter of a triangle is the sum of the lengths of its sides. We will calculate the lengths of segments AB, AC, and BC using the distance formula:
    • The distance formula between two points (x1, y1) and (x2, y2) is given by: d = √((x2 - x1)² + (y2 - y1)²)
  3. Calculate AB:
    • Using points A(3, 0) and B(0, 4):
    • AB = √((0 - 3)² + (4 - 0)²) = √(9 + 16) = √25 = 5
  4. Calculate AC:
    • Using points A(3, 0) and C(3, 0):
    • AC = √((3 - 3)² + (0 - 0)²) = √(0 + 0) = √0 = 0
  5. Calculate BC:
    • Using points B(0, 4) and C(3, 0):
    • BC = √((3 - 0)² + (0 - 4)²) = √(9 + 16) = √25 = 5

Now we have the lengths of the sides:

  • AB = 5
  • AC = 0
  • BC = 5

Finally, we can calculate the perimeter:

Perimeter = AB + AC + BC = 5 + 0 + 5 = 10

Therefore, the perimeter of triangle ABC is 10 units.

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