Final answer:
Using the Pythagorean theorem, the length of side AC in right triangle ABC with vertices A(3, -5), B(0, -5), and C(3, 2) is calculated as 7 units since the vertical leg is 7 units long and the horizontal leg is 0 units.
Step-by-step explanation:
To find the length of side AC in the right triangle ABC, where A(3, -5), B(0, -5), and C(3, 2), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c = √(a² + b²).
Here, we can consider AC as the hypotenuse. To calculate the lengths of the legs, we look at the coordinates. The change in y (vertical distance) between points A and C is from -5 to 2 which is 7 units. The change in x (horizontal distance) is from 3 to 3, which is 0 units, since they lie on the same vertical line. Plugging these into the formula, we get: AC = √((0 units)² + (7 units)²) = √(49) = 7 units.
Therefore, the length of side AC in the right triangle ABC is 7 units.