Final answer:
The perimeter of the right triangle with vertices A(6, 0), B(0, 0), and C(0, 8) is calculated using the lengths of the sides AB and BC, and the Pythagorean Theorem to find the hypotenuse AC. The sum of the lengths AB (6 units), BC (8 units), and AC (10 units) gives us a perimeter of 24 units.
Step-by-step explanation:
To find the perimeter of the right triangle with coordinates A(6, 0), B(0, 0), and C(0, 8), we'll need to use the Pythagorean Theorem which is stated as a² + b² = c², and in our case, can be rewritten as c = √a² + b². The lengths of the sides can be found by calculating the difference in the x-coordinates for the horizontal leg AB, and the difference in the y-coordinates for the vertical leg BC. Finally, for the hypotenuse AC, we apply the Pythagorean theorem.
AB = 6 units (difference in x-coordinates between A and B)
BC = 8 units (difference in y-coordinates between B and C)
To find AC, we use:
AC = √(AB² + BC²)
AC = √(6² + 8²)
AC = √(36 + 64)
AC = √100
AC = 10 units
The perimeter is the sum of all three sides, so:
Perimeter = AB + BC + AC
Perimeter = 6 units + 8 units + 10 units
Perimeter = 24 units
Therefore, the correct answer is c) 24 units.