In right triangle $ABC$, angle $B$ is the right angle, $A$ is at the origin, $B$ is at $(0,4)$, and $C$ is at $(3,0)$. What is the length of line segment $AC$? Round to the nearest tenth.

• A. $4.0$
• B. $3.0$
• C. $7.0$
• D. $5.0$

Answer: (D)

Verified step by step guidance

1. Identify the coordinates of points A, B, and C: A is at (0, 0), B is at (0, 4), and C is at (3, 0).
2. Recognize that triangle ABC is a right triangle with the right angle at B, so sides AB and BC are perpendicular and can be considered as legs of the triangle.
3. Calculate the length of segment AB using the distance formula between points A(0,0) and B(0,4): \(\text{AB} = \sqrt{(0-0)^2 + (4-0)^2}\).
4. Calculate the length of segment BC using the distance formula between points B(0,4) and C(3,0): \(\text{BC} = \sqrt{(3-0)^2 + (0-4)^2}\).
5. Use the Pythagorean theorem to find the length of segment AC (the hypotenuse): \(\text{AC} = \sqrt{\text{AB}^2 + \text{BC}^2}\).