ACT (Enhanced)MathematicsMedium
A robotics engineer is programming a robot arm to move in a straight line. The arm starts at point A (2, 3) and moves to point B (6, 6). What is the length of the path the robot arm travels?
- A5 units
- B3 units
- C4 units
- D7 units
Show answer & explanationAnswer & explanation
Correct answer: A. 5 units
The length of the path is the distance between points A and B. Use the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. Here, (x₁, y₁) = (2, 3) and (x₂, y₂) = (6, 6). d = √[(6 - 2)² + (6 - 3)²] = √[(4)² + (3)²] = √[16 + 9] = √25 = 5 units.
Why the other options are wrong
- B. This is the difference in y-coordinates only.
- C. This is the difference in x-coordinates only.
- D. This is the sum of the absolute differences in x and y coordinates (4+3), not the Euclidean distance.
Distance Formula (2D)
A formula used to calculate the straight-line distance between two points (x₁, y₁) and (x₂, y₂) in a Cartesian coordinate system.
- Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²].
- Derived from the Pythagorean theorem.
- Always yields a non-negative value.
Memory trick: Distance Route: Subtract X's, subtract Y's, square, add, then square root!