ACT (Enhanced)MathematicsMedium
A pilot is planning a flight between two cities. City A is located at coordinates (10, 20) and City B is located at (40, 60) on a grid map, where units are in miles. What is the straight-line distance, in miles, between City A and City B?
- A30 miles
- B50 miles
- C40 miles
- D70 miles
Show answer & explanationAnswer & explanation
Correct answer: B. 50 miles
The distance formula is d = √((x2 - x1)² + (y2 - y1)²). Given (x1, y1) = (10, 20) and (x2, y2) = (40, 60). So, d = √((40 - 10)² + (60 - 20)²) = √((30)² + (40)²) = √(900 + 1600) = √(2500) = 50 miles.
Why the other options are wrong
- A. This is the difference in x-coordinates only.
- C. This is the difference in y-coordinates only.
- D. This is the sum of the absolute differences in x and y coordinates, not the straight-line distance.
Distance Formula (2D)
The distance formula calculates the straight-line distance between two points (x1, y1) and (x2, y2) in a two-dimensional 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: difference of Xs squared, plus difference of Ys squared, all under a root.